### Workshop

#### Bootstrapping Nature: Non-perturbative Approaches to Critical Phenomena

**Oct 03, 2022 - Nov 04, 2022**

**Abstract**

Critical phase transitions are ubiquitous in nature, as they describe both classical statistical systems such as the water/vapor transition, as well as quantum systems such as superfluid transitions. These phase transitions are difficult to study, because the quantum field theories that describe them are generically strongly coupled, and traditional methods like Feynman diagrams do not suffice. Recently, new non-perturbative tools such as the conformal bootstrap and duality have been used to study strongly coupled phase transitions, which complements non-perturbative methods such as lattice Monte Carlo. This workshop will bring together scientists from the neighboring communities of condensed matter and high energy theory to identify new continuous phase transitions that appear in nature, especially those with emergent gauge fields, and develop strategies to solve these systems and guide ongoing experiments.

**Topics**

* Critical phase transitions

* Numerical conformal bootstrap

* Lattice methods

* Dualities

* Gauge theories in 2+1 dimensions

TRAINING WEEK

The first week of the workshop consists in a school with pedagogical lectures on the following topics:

* Intro to CFT and conformal bootstrap (Andreas Stergiou, King's College London)

* Intro to lattice methods for phase transitions (Anders Sandvik, Boston University)

* Intro to gauge theories in 2+1 dimensions and dualities (Chong Wang, Perimeter Institute)

CONFERENCE

The third week of the workshop consists in a focus week, with a more intese schedule of talks.

STREAMING AND RECORDINGS

Lectures and conference talks will be recorded and uploaded on this page every day. To watch the video streaming of the talks live please email the organisers.

**Organizers**

Shai Chester (Harvard U.);

Ribhu Kaul (U. of Kentucky);

Subir Sachdev (Harvard U.);

Alessandro Vichi (U. of Pisa);

Chong Wang (Perimeter Institute);

William Witczak-Krempa (U. of Montreal);

**Contact**

alessandro.vichi@unipi.it

iahs81@gmail.com

**Talks**

Date | Speaker | Title | Type | Useful Links | ||||
---|---|---|---|---|---|---|---|---|

Oct 03, 2022 - 09:00-10:45 | Andreas Stergiou |
Introduction to CFT and Conformal Bootstrap | Lecture | Video | ||||

Oct 03, 2022 - 11:15-13:00 | Chong Wang |
Gauge theories in 2+1 dimensions and dualities | Lecture | Video | ||||

Oct 03, 2022 - 15:00-16:45 | Anders Sandvik |
Lattice models and numerical simulations | Lecture | Slides | Video | |||

Oct 04, 2022 - 09:00-10:45 | Andreas Stergiou |
Introduction to CFT and Conformal Bootstrap | Lecture | Video | ||||

Oct 04, 2022 - 11:15-13:00 | Chong Wang |
Gauge theories in 2+1 dimensions and dualities | Lecture | Video | ||||

Oct 04, 2022 - 15:00-16:45 | Anders Sandvik |
Lattice models and numerical simulations | Lecture | Slides | Video | |||

Oct 05, 2022 - 09:00-10:45 | Andreas Stergiou |
introduction to CFT and Conformal Bootstrap | Lecture | Video | ||||

Oct 05, 2022 - 11:15-13:00 | Chong Wang |
Gauge theories in 2+1 dimensions and dualities | Lecture | Video | ||||

Oct 05, 2022 - 15:00-16:45 | Anders Sandvik |
Lattice models and numerical simulations | Lecture | Slides | Video | |||

Oct 06, 2022 - 09:00-10:45 | Andreas Stergiou |
Introduction to CFT and Conformal Bootstrap | Lecture | Video | ||||

Oct 06, 2022 - 11:15-13:00 | Chong Wang |
Gauge theories in 2+1 dimensions and dualities | Lecture | Video | ||||

Oct 06, 2022 - 15:00-16:45 | Anders Sandvik |
Lattice models and numerical simulations | Lecture | Slides | Video | |||

Oct 07, 2022 - 09:00-10:45 | Andreas Stergiou |
Introduction to CFT and Conformal Bootstrap | Lecture | Video | ||||

Oct 07, 2022 - 11:15-13:00 | Chong Wang |
Gauge theories in 2+1 dimensions and dualities | Lecture | Video | ||||

Oct 07, 2022 - 15:00-16:45 | Anders Sandvik |
Lattice models and numerical simulations | Lecture | Slides | Video | |||

Oct 10, 2022 - 11:00-12:15 | Rajeev Erramilli |
The O(N) Gross-Neveu-Yukawa Archipelago | Talk |
Abstract
I will present numerical results from conformal bootstrap studies of four-point correlation functions of fermions and scalars in 3D CFTs with O(N) symmetry. This work comes as a culmination of an effort to expand the practical scope of the numerical bootstrap to correlators with generic spinning operators. As such, I will also present how we derive our numerical setup. Our results provide rigorous bounds on scaling dimensions and OPE coefficients of the O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We find that the N=1 case, as expected, shows a supersymmetric enhancement. Finally, I will argue the distinction between the O(N) GNY fixed points and the Chiral Ising universality class. |
Slides | |||

Oct 11, 2022 - 11:00-12:15 | Hugh Osborn |
Finding fixed points in the epsilon expansion | Talk | |||||

Oct 12, 2022 - 11:00-12:15 | Akshat Pandey |
A stability bound on T-linear resistivity | Talk |
Abstract
Analyses of transport data in metals, both conventional and prima facie unconventional, have suggested that the slope of linear-in-temperature resistivity is bounded from above, leading to many theoretical proposals for fundamental “Planckian” bounds on dissipation and thermalization in metals. We identify the origin of the bound in conventional metals, and associate it with a crossover into an insulating regime when interactions are strong. We then speculate on a new line of attack on the observed bounds more generally, namely that they reflect a limit to interaction strengths between low-energy modes consistent with the stability of a metallic state. |
||||

Oct 13, 2022 - 11:00-12:15 | Joshua Sandor |
Anyon Scattering from Lightcone Hamiltonian: the Singlet Channel | Talk |
Abstract
We study U(N) Chern-Simons theory coupled to massive fundamental fermions in the lightcone Hamiltonian formalism. Focusing on the planar limit, we introduce a con- sistent regularization scheme, identify the counter terms needed to restore relativistic invariance, and formulate scattering theory in terms of unambiguously defined asymp- totic states. We determine the 2 → 2 planar S-matrix element in the singlet channel by solving the Lippmann-Schwinger equation to all orders, establishing a result previously conjectured in the literature. Based on arXiv: 2205.09144 |
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Oct 14, 2022 - 11:00-12:15 | Ryan Lanzetta |
Bootstrapping Lieb-Schultz-Mattis anomalies | Talk |
Abstract
The Lieb-Schultz-Mattis (LSM) theorem and its generalizations provide criteria for the symmetries of lattice models which, when met, preclude the lattice model from being trivially gapped. These results can be interpreted in more modern terms as a special case of anomaly matching of a mixed “LSM anomaly” between a spatial symmetry and an internal symmetry. I will present recent work that uses conformal bootstrap to obtain universal bounds on (1+1)d CFTs that can describe bosonic spin chains possessing certain LSM anomalies in the infrared. The approach I will introduce combines both modular bootstrap and correlator bootstrap of symmetry defect operators, and in certain cases this approach is essential for finding any bounds at all. Time permitting, I will discuss applications of my bounds to the theory of phase transitions of (1+1)d symmetry protected topological phases. |
Slides | |||

Oct 17, 2022 - 09:30-10:30 | Marten Reehoorst |
Navigating Outer Space | Talk |
Abstract
The numerical conformal bootstrap has been very successful in bounding CFT data resulting in precise determinations of quantities such as critical exponents in second order phase transitions. However, until recently, the numerical bootstrap could only be applied to problems involving a handful of parameters at most. I will discuss how we introduced a Navigator function (https://arxiv.org/abs/2104.09518) to solve this problem and how I applied these new methods to find bounds in high dimensional parameter spaces (https://arxiv.org/abs/2111.12093). I show that these methods massively outperform traditional methods by applying them to obtaining new rigorous bounds on various quantities in the 3d Ising model. This results, among others, in the first rigorous and precise determination of the ω-exponent controlling the leading correction to scaling. Comparing my rigorous results with the non-rigorous estimates obtained by the Extremal Functional Method I find a good match for both the central values and the error estimates, thus validating the EFM. Finally, I also explore the influence of new kind of sparseness assumption which previously could not be studied. |
Slides | Video | ||

Oct 17, 2022 - 11:30-12:30 | Ning Su |
Recent development in bootstrap numerics | Talk |
Abstract
I will overview a few bootstrap studies on Ising, cubic, and Potts models. Those studies show promising results that are relevant for statistical physics problems. However, in order to draw a sharp conclusion, we still have to further push the numerics in the future, which is very challenging with current technology. I will present a new numerical method that can significantly improve the numerics of large scale bootstrap problems. |
Slides | Video | ||

Oct 17, 2022 - 14:00-15:00 | Zhijin Li |
Cracking the critical flavor number of QED3 with conformal bootstrap | Talk |
Abstract
Three dimensional quantum electrodynamics (QED3) coupled to fermions is expected to have a critical flavor number of fermions, which separates the conformal phase from the chiral symmetry breaking phase in the infrared limit. The critical flavor number has been extensively studied in the past decades without a conclusive answer. In this talk, I will show that the conformal bootstrap can shed new light for this long-standing problem. I will firstly show that the widely interested SO(5)/O(4) symmetric deconfined quantum critical points are just below a new family of kinks in the SO(N) vector bootstrap bounds, while the lattice and perturbative estimates of the critical indices can be excluded by the bootstrap bounds associated with few reasonable assumptions on the spectrum. Then I will explain a remarkable algebraic structure in the bootstrap crossing equations and its fundamental role in bootstrap studies. I will show that the bootstrap bounds are nearly saturated by conformal QED3 after introducing assumptions relevant to conformal QED3. In particular the CFT data of four flavor QED3 can be isolated into a closed region and the bootstrap bounds are beautifully consistent with some large Nf perturbative results. The bootstrap results suggest the critical flavor number of QED3 is slightly above 2 while below 4. I will discuss some predictions and new problems that arose in bootstrap studies. |
Slides | |||

Oct 17, 2022 - 15:15-16:15 | Pedro Liendo |
Bootstrapping line defects with O(2) global symmetry | Talk |
Abstract
We discuss 1d conformal line defects with O(2) symmetry using the numerical bootstrap. We start with an agnostic approach and perfom a systematic bootstrap study of correlation functions of two canonical defect operators: the displacement and the tilt, without making any assumptions regarding the spectrum of the theory. We then move on to study two specific models: a monodromy line defect and a localized magnetic field line defect, where we use analytic input coming from an epsilon-expansion analysis. The interplay between analytical and numerical techniques gives intriguing results which we explore. |
Slides | Video | ||

Oct 18, 2022 - 09:30-10:30 | Gabriel Cuomo |
Charged spinning operators in CFTs: from superfluids to Regge theory | Talk |
Abstract
In CFT, states with large quantum numbers often admit a simple universal description. Most famously, CFTs become approximately free in the large spin sector, with operators organized in Regge trajectories labeled by the twist. On the other hand, operators with large quantum numbers under the internal symmetries of the theory often admit an effective hydrodynamic description. In this talk, I will review these results and I will propose a series of EFT descriptions for operators with both large charge and large spin in 3d CFTs. The results smoothly interpolate between the hydrodynamic regime and the large spin Regge theory. Based on 1711.02108 with A. De la Fuente, A. Monin, D. Pirtskhalava, R. Rattazzi, and on work in progress with Z. Komargodski. |
Slides | Video | ||

Oct 18, 2022 - 11:30-12:30 | Luca Delacretaz |
Nonlinear bosonization of Fermi liquids | Talk |
Abstract
Landau's theory of Fermi liquids is a cornerstone of theoretical physics. I will show how to formulate Fermi liquid theory as an effective field theory of bosonic degrees of freedom. While at the linear level, this theory reduces to existing bosonization approaches, it necessarily features nonlinear corrections that are fixed by the geometry of the Fermi surface. These are crucial to reproduce nonlinear response, such as higher-point functions of currents. The effective field theory framework furthermore systematically parametrizes corrections to Fermi liquid behavior, and provides a computationally advantageous approach for non-Fermi liquids -- strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions. |
Slides | Video | ||

Oct 18, 2022 - 14:00-15:00 | David Mross |
Spin-charge fractionalization in two dimensions from duality | Talk |
Abstract
Strong interactions between spin-1/2 particles may cause them to split into spinless chargon and charge-neutral spinons. In my talk, I will demonstrate that an effective field theory of such excitations directly follows from the long-wavelength structure of vortices close to a Mott transition. This mapping between microscopic and fractional excitations can be realized exactly in a coupled-wire array and used to generate parent Hamiltonians for numerous exotic phases. I will relate the duality introduced here to parton approaches and discuss possible extensions to other two and and-dimensional systems. |
Slides | Video | ||

Oct 18, 2022 - 15:15-16:15 | Zohar Komargodski |
Defects, One-Form Symmetry, and RG Flows | Talk |
Abstract
We discuss constraints on renormalization group flows on line defects (impurities). First we consider the implications of one-form symmetry and then we consider the implications of a new entropy function. We give some examples from impurities in magnets and in gauge theories in 2+1 and 3+1 dimensions. |
Slides | Video | ||

Oct 18, 2022 - 17:00-18:00 | Shai Chester |
Evidence for 3d bosonization from monopole operators | Talk |
Abstract
We give evidence for 3d bosonization by computing monopole operator scaling dimensions in 2+1 dimensional quantum electrodynamics (QED3) with Chern-Simons level k and N complex scalars in a semiclassical expansion. We first consider the k=0 case, where we show that scaling dimensions previously computed to subleading order in 1/N can be extrapolated to N=1 and matched to O(2) Wilson-Fisher scaling dimensions with less than 5% error, which is a precise check of particle-vortex duality. We then generalize the subleading calculation to large N,k and fixed k/N, extrapolate to N=k=1, and consider monopole operators that are conjectured to be dual to non-degenerate scalar operators in a theory of a single complex fermion. We find matches with less than 2% error, which are a precise check of this so-called 'seed' duality that implies a web of 3d bosonization dualities. |
Slides | Video | ||

Oct 19, 2022 - 09:30-10:30 | Bernardo Zan |
Chiral symmetry and mass shift for the lattice Schwinger model | Talk |
Abstract
The Schwinger model is one of the simplest gauge theories, yet it is only solvable in the massless case. In order to obtain numerical results, the Kogut-Susskind lattice approach with staggered fermion is regularly used. I will show that, contrary to what it was believed, the lattice mass and the continuum mass are actually not the same, but they are related by a mass shift. This can be understood by considering the (anomalous) chiral symmetry in the massless case, and has the advantage of greatly improving convergence of the numerics. I will comment on the charge-q Schwinger model as well as the multiflavor Schwinger model as well. |
Slides | Video | ||

Oct 19, 2022 - 11:30-12:30 | Anders Sandvik |
Multi-critical deconfined quantum-critical point: numerics and experiments | Talk |
Abstract
The concept of the deconfined quantum critical point (DQCP) has greatly influenced condensed matter theories during the past couple of decades, yet controversies remain and experimental realizations have been lacking. Here I will discuss a variant of the original proposal in which a multi-critical DQCP separates a gapless spin liquid phase and a line of first-order transitions between antiferromagnetic (AFM) and valence-bond solid (VBS) phases. Evidence for this scenario comes from quantum Monte Carlo studies of J-Q models, which show the presence of two relevant symmetric operators at the critical point. Moreover, DMRG studies of frustrated spin models have revealed a spin liquid phase between their AFM and VBS ground states, and when tuning additional couplings the spin liquid terminates and is followed by a direct AFM-VBS transition. I will also discuss recent heat capacity and NMR experiments on the layered quantum magnet SrCu$_2$(BO$_3$)$_2$ under high pressure and external magnetic field. The material is well described by the Shastry-Sutherland spin-1/2 model, which is one of the models in which the spin liquid and multi-critical DQCP scenario has been explored. At pressures above 2 GPa, the experiments demonstrate a field driven transition between VBS (of the plaquette type) and AFM phases at low temperatures (below 0.07 K). First-order signatures of the transition weaken with increasing pressure, and at the highest accessible pressure (2.4 GPa) the spin-lattice relaxation rate shows quantum-critical scaling versus the temperature. These observed behaviors fit with the scenario of a proximate multi-critical DQCP and also open the intriguing prospect of a spin liquid phase in zero field at slightly higher pressures. |
Slides | Video | ||

Oct 19, 2022 - 14:00-15:00 | Martin Hasenbusch |
Monte Carlo study of improved lattice models in three dimensions | Talk |
Abstract
We study the critical behavior of lattice models in three dimensions by using Monte Carlo simulations combined with a finite size scaling analysis of the data. The parameters of the models are tuned such that leading corrections to scaling vanish. Based on these results, accurate estimates of universal quantities such as critical exponents are obtained. Here we discuss the lattice models that are studied, the Monte Carlo algorithms that are employed and the theoretical basis of the data analysis. We summarize results that have been obtained for the Ising, the XY and the Heisenberg universality classes and compare them with results obtained by other methods. |
Slides | Video | ||

Oct 19, 2022 - 17:00-18:00 | Fredric Mila |
Conformal Field Theory and Chiral Melting in 2D | Talk |
Abstract
Continuous phase transitions in 2D usually fall in the universality class of one of the minimal models of 2D conformal field theory. Commensurate melting is an exception, and for phases with periodicity 5 or larger, the transition is generically a Pokrovsky-Talapov one into a critical phase with anisotropy (or dynamical) exponent z=2. For systems with periodicity 3 or 4, the even more exotic possibility of a chiral transition has been put forward by Huse and Fisher in 1982, who suggested that the transition could be continuous and directly into a disordered phase, but with an anisotropy exponent z >1. This problem, which has been left unsolved in the eighties, with numerical papers reaching opposite conclusions, has recently resurfaced in 1D quantum models in the context of chains of Rydberg atoms. In this talk, I will present recent numerical results on 1D quantum and 2D classical models of commensurate melting that provide strong evidence in favour of a chiral transition. All these results have been obtained using tensor network based approaches that were not available in the eighties. I will also argue that the possibility of a chiral transition, which predates the discovery of the minimal models of 2D CFT, might actually be supported by CFT for p=3 as a necessary intermediate phase between a conformal transition in the 3-state Potts universality class with central charge c=4/5 and a critical phase with central charge c=1. |
Slides | Video | ||

Oct 20, 2022 - 09:30-10:30 | Miguel Paulos |
Bootstrapping Bulk Locality | Talk |
Abstract
We revisit the problem of constructing bulk fields from boundary CFT data. Any such field admits a boundary operator expansion (BOE) which must be delicately tuned so that fields have local correlators. The first non-trivial constraints appear at the level of three point functions involving a bulk field and two boundary operators. In this case we recast the constraints of locality as a set of sum rules on the BOE data. These sum rules can be obtained either by acting with a complete basis of linear functionals, or by demanding that correlators admit an expansion in terms of manifestly local functions which we dub ``local blocks'', and which have a simple interpretation in terms of AdS Witten diagrams. We show that the sum rules allow us to easily reconstruct local perturbative correlators in AdS/CFT. More generally, the language of functionals allow us to discuss properties of generic ``interacting'' solutions to the locality problem and the structure of the BOE. Finally we discuss how in the flat space limit the locality problem maps onto the question of constructing local form factors from knowledge of the S-matrix. |
Video | |||

Oct 20, 2022 - 11:30-12:30 | Subir Sachdev |
Quantum statistical mechanics of charged black holes and strange metals | Talk |
Abstract
The Sachdev-Ye-Kitaev model is an illuminating example of a CFT in 0+1 dimensions. All such CFTs have a protected “energy” operator whose perturbations are irrelevant at energy scales much below J, where J is a UV cutoff. However, at even lower energy scales below J/(total entropy), this operator becomes dangerously irrelevant, and its fluctuations are described by a universal theory of quantum gravity in 1+1 dimensions. Remarkably, the same gravity theory also describes the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. Time permitting, I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems. |
Slides | Video | ||

Oct 20, 2022 - 14:00-15:00 | Petr Kravchuk |
Detectors in Weakly-Coupled Field Theories | Talk |
Abstract
One of the main aspects of any CFT is its spectrum of local operators. The scaling dimensions and spins of local operators are believed to lie on analytic curves known as Regge trajectories. Points on the Regge trajectories in between the local operators correspond to non-local light-ray operators. In this talk I will discuss the relationship between the light-ray operators and asymptotic detectors in conformal colliders. Using this correspondence, we will study Regge trajectories in the epsilon-expansion of the Wilson-Fisher fixed point and show that a novel type of horizontal trajectories contributes to correlation functions in the Regge limit. Based on https://arxiv.org/abs/2209.00008. |
Video | |||

Oct 20, 2022 - 15:15-16:15 | Balt Van Rees |
RG flows in AdS | Talk |
Abstract
The boundary correlation functions of QFTs in AdS are generically conformal, even if the bulk theory is not. This allows one to use d-dimensional conformal bootstrap methods to study RG flows in one dimension higher. We will discuss some analytic and numerical insights, with a focus on the flow between the diagonal unitary minimal models in AdS_2. |
Slides | Video | ||

Oct 20, 2022 - 17:00-18:00 | Yin-Chen He |
Spotting conformal symmetry of 3D Ising transition: a gift from quantum fuzziness | Talk |
Abstract
I will talk about our work on simulating 3D Ising transition on the spherical geometry, i.e. S^2 x R. For the first time we have observed almost perfect state-operator correspondence of 3D Ising transition (on a very small system size!), hence directly supports the conjecture that 3D Ising transition being conformal. Our approach is based on an exotic way of regularizing 3D Ising transition using spherical Landau levels. In other words, our model is defined on a fuzzy (non-commutative) sphere, which is the key of the success. Our result may open a new avenue of studying 3D CFTs beyond the conventional lattice model simulations. |
Slides | Video | ||

Oct 21, 2022 - 09:30-10:30 | Marco Meineri |
An extraordinary boundary condition from the conformal bootstrap | Talk |
Abstract
I will discuss the critical behavior of the O(N) model with a boundary. In three dimensions, when the boundary coupling is enhanced, the long distance physics was recently found to depend on N. When N is less than a critical value N_c, logarithmic corrections arise in correlation functions, signaling the attempt of the system to spontaneously break the symmetry. As I will review, the attempt is not quite successful and the symmetry survives. The value of N_c is not known. I will describe how to use the bootstrap to constrain it, and give evidence for the critical value being above 3, and in fact close to 5. |
Video | |||

Oct 21, 2022 - 11:30-12:30 | Juchen Rong |
Conformal field theory approach to quantum loop models | Talk |
Abstract
We study the quantum loop model on the triangular lattice. In the continuum limit, the phase transition between the Z2 spin liquid phase and a certain solid phase with broken translational symmetry can be understood as a quantum field theory of three scalars coupled together. The results of the conformal bootstrap study of the O(3) vector model play an important role in understanding the quantum Monte Carlo simulation result of the model, and in clarifying the phase diagram. If time permits, I will also discuss a similar story about the quantum loop model on a square lattice. |
Slides | Video | ||

Oct 21, 2022 - 14:00-15:00 | Ryan Thorngren |
Gapless SPTs | Talk |
Abstract
A lot of progress has been made in the classification of gapped phases of matter from the perspective of topological quantum field theory, especially in the realm of symmetry protected topological (SPT) phases. Much less is known about gapless phases. In this talk I will describe a program based on understanding the role symmetry plays in these phases. I will first describe coexistence phases where SPT physics persists in the presence of gapless modes, and especially the fate of the SPT edge modes. Then I will describe recent progress in "intrinsically gapless" phases, which show behavior not possible in a gapped phase. |
Slides | |||

Oct 21, 2022 - 15:15-16:15 | Zhen Bi |
Measurement-Prepared Quantum Phases and Phase Transitions: from Ising model to gauge theory, and beyond | Talk |
Abstract
In condensed matter physics, we usually think about quantum phases and phase transitions in the context of equilibrium many-body system. In this talk, we consider a slightly different setup to prepare quantum phases and phase transitions with shallow quantum circuit and measurements. First, I will talk about ways one can prepare interesting quantum states, including topological order, symmetry breaking state, etc., by measuring a so-called resource state. Then I will show that with post-selection one can tune a phase transition between certain quantum states by changing a continuous parameter in the measurements. This measurement-prepared quantum critical state corresponds to the so-called conformal quantum critical points where the equal-time correlators exhibit spatial conformal invariance. This establishes an exact correspondence between the measurement-prepared critical states and conformal field theories of a range of critical spin models, including familiar Ising models and gauge theories. Without post-selection, we can show the correspondence between the ensemble of quantum states prepared by measurements and the ensemble of the ferromagnetic RBIM along the special path called Nishimori line. Our findings suggest a novel mechanism in which a quantum critical wavefunction emerges, providing new practical ways to study quantum phases and conformal quantum critical points. |
Slides | Video | ||

Oct 21, 2022 - 17:00-18:00 | Cenke Xu |
An exotic metal-insulator transition and a quantum bad metal | Talk |
Abstract
The electrical conductivity/resistivity of a two dimensional ( 2+1d ) system is a dimensionless quantity, and in many cases can be universal (such as the conductivity at various 2+1d quantum critical points). Previous theories for metal-insulator transitions (MIT) of 2D electron systems (either driven by disorder or interaction) predicted a critical resistivity at the order of h/e^2. Recent experiment on the transition metal dichalcogenide (TMD) moiré heterostructures reported a continuous MIT driven by interaction, where the critical resistivity at low temperature is exceedingly larger than h/e^2, which calls for a new theory. We propose a theory for the exotic MIT, with fractionalization of electric charges, which naturally leads to a large critical resistivity. We will also construct a metallic phase with strongly interacting electrons, which enjoys a perturbative description in terms of the dual vortex degree of freedom. We demonstrate that when the vortices form a Fermi liquid (a good metal), the electrical resistivity of the metallic phase at low temperature is far beyond the so-called Mott-Ioffe-Regal limit. Other features of the exotic MIT and the metallic phase will be discussed. |
Slides | Video | ||

Oct 24, 2022 - 11:30-12:30 | Stefanos Kousvos |
Bootstrapping Deformations of O(n) | Talk |
Abstract
In this talk I will argue that most scalar field theories of interest due to critical phenomena can be written as a deformation of O(n). I will discuss deformations of O(n) first at a Hamiltonian/Lagrangian level, and then at the level of projectors and invariant tensors. The first viewpoint is useful for building intuition, whereas the second concerns the precise objects that inject the conformal bootstrap with information about the global symmetry. Having laid out this groundwork, I will present a series of results regarding a number of theories relevant for physics. The validity of both the Large-n and ε-expansions for studying such theories will be discussed. I will conclude by discussing the outlook for the near future and some directions that are currently being pursued. |
Video | |||

Oct 25, 2022 - 15:30-16:45 | Barak Gabai |
Bootstrapping the Ising Model on the Lattice | Talk |
Abstract
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous two-sided bounds on spin correlators through semi-definite programming. For the 2D Ising model on the square lattice, the bootstrap bounds based on correlators supported in a 13-site diamond-shaped region determine the nearest-spin correlator to within a small window, which for a wide range of coupling and magnetic field is narrower than the precision attainable with Monte Carlo methods. We also report preliminary results of the bootstrap bounds for the 3D Ising model on the cubic lattice. |
Video | |||

Oct 26, 2022 - 11:30-12:30 | Slava Rychkov |
The fate of Parisi-Sourlas Supersymmetry in Random Field Ising model | Talk |
Abstract
I will review the status of Parisi-Sourlas supersymmetry in the Random Field Ising model, in the related model of branched polymers. Our recent work shows that supersymmetry is lost for RFIM for d |
Video | |||

Oct 27, 2022 - 11:30-12:30 | Zhenjiu Wang |
Quantum Monte Carlo simulation of skyrmion superconductivity | Talk |
Abstract
A quantum spin Hall (QSH) insulating state that arises from spontaneous symmetry breaking has remarkable properties: skyrmion textures of the SO(3) order parameter carry charge 2e. Two new routes to superconductivity from the QSH state is approached either via tuning interaction at particle-hole symmetric point or via doping. We define a model amenable to large-scale negative sign free quantum Monte Carlo simulations that allows us to study this transition. Our results support two direct and continuous transitions between quantum spin Hall insulator and an s-wave superconductor: a deconfined quantum critical point and a doping induced superconductor via skyrmion condensation. |
Video | |||

Oct 28, 2022 - 11:30-12:30 | Simon Hands |
Quantum Criticality in the 2+1d Thirring Model | Talk |
Abstract
The Thirring Model is a covariant quantum field theory of interacting fermions, sharing many features in common with effective theories resembling QED in 2+1 dimensions, proposed to describe layered electronic systems with linear dispersion such as graphene. For a small number of flavors and sufficiently strong interactions the ground state may be disrupted by condensation of particle-hole pairs, leading to the dynamical generation of a fermion massgap. With no small dimensionless parameters in play in this regime the Thirring model is plausibly the simplest theory of fermions requiring a numerical solution. I will review what is currently known focussing on recent lattice field theory simulations employing Domain Wall Fermions, a formulation drawn from lattice QCD, to faithfully capture the underlying symmetries of the strong dynamics at the critical point. Results will be presented for both the bilinear order parameter and the spectrum, suggesting that for the single flavor theory there is indeed a quantum critical point with a large anomalous scaling dimension for the fermion field. |
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Nov 02, 2022 - 11:30-12:30 | Connor Behan |
Coupled minimal models revisited | Talk |
Abstract
It is widely believed that two copies of the 3d Ising model, coupled via their energy operators, will flow to the O(2) model in the IR. In two dimensions, one also has the option of coupling higher minimal models together. These offer a number of underexplored possibilities for triggering RG flows that are arbitrarily weakly coupled. I will give an overview of the zoo of fixed points one can obtain. Importantly, some of the tools most helpful for analyzing them did not exist ten years ago. I will focus on multiplet recombination and what it can tell us about the (ir)rationality of these CFTs. |
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Nov 02, 2022 - 14:00-15:00 | Ilya Gruzberg |
TBA | Talk | |||||

Nov 02, 2022 - 15:00-16:00 | Jaychandran Padayasi |
On CFTs with Abelian OPE in d ≥ 2 | Talk |
Abstract
In 2d CFTs, an Abelian fusion rule is understood as the case when only one Virasoro primary is exchanged in the OPE. The canonical exam- ple is the fusion algebra of vertex operators constructed out of the free boson, with the fusion rule Vα1 ×Vα2 ∼Vα1+α2. We study the meaning of Abelian fusion in terms of the global conformal blocks in 2d, and generalize the resulting understanding to d > 2, where one doesn’t have the Virasoro structure. In the process, we derive a generalization of the Vafa-Lewellen constraints, that restrict the spectrum ∆(α) of a closed, Abelian CFT labeled by a parameter α to be quadratic in that parameter. Our in- vestigations are motivated by the usefulness of Abelian CFTs for describing conformally invariant multifractal measures, such as the scaling of the moments of the critical wavefunction at the Anderson transitions. |
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Nov 03, 2022 - 11:30-12:30 | Soner Albayrak |
Inverting the 3d Fermions | Talk |
Abstract
The 6j symbols of the fermion representations encode kinematic data that can be used with the crossing symmetry to generate relations and constraints in the spectrum of CFTs with fermionic operators. Yet these symbols are themselves tightly constrained by the conformal symmetry and can be reconstructed from their counterparts for the scalar operators via a judicious application of the weight shifting operators. In this talk, we will review how these technologies can be combined to yield an effective inversion formula for fermionic spectrum, and how this approach can be generalized to other spinning operators. |
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Nov 03, 2022 - 14:00-15:00 | Claudio Bonanno |
Benchmarking the Ising Universality Class in 3 ≤ d < 4 dimensions | Talk |
Abstract
I will present results for the Ising critical exponents in dimensions 3 ≤ d < 4 by numerical conformal bootstrap. Given the one-per-thousand accuracy, they can provide a benchmark for future studies of critical phenomena in varying dimension. I will also outline a detailed comparison with perturbation theory close to d = 4 and with other bootstrap setups and resummed epsilon-expansion in the non-perturbative regime. Finally, I will also present accurate results for other operators, as well as for structure constants, which are determined even better than dimensions. |
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Nov 04, 2022 - 11:30-12:30 | Giacomo Gori |
Trading algebra for geometry in d>2 critical systems | Talk |
Abstract
We discuss how a geometric approach to the symmetries of a critical system leads to novel predictions for the structure of correlations in generic d>2 bounded systems at criticality. Questions that can be tackled with this mindset are: How does the ordered state on the surface penetrate into a critical bulk? Does a two-point function depend fully on the position of both points or it actually depends on a reduced number of relevant variables? The answer will entail defining and solving a fractional version of the Yamabe problem making an anomalous curvature constant. The validity of this framework (which we dub Critical Geometry) is put to test in a wide and representative range of statistical models. |
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Nov 04, 2022 - 14:00-15:00 | Shailesh Chandrasekharan |
Quantum field theories via qubit regularization of lattice spin and gauge models | Talk |
Abstract
Motivated by the goal of studying continuum quantum field theories on a quantum computer, we explore a new type of lattice regularization of quantum field theories, called qubit regularization. We propose a systematic method to construct qubit regularized lattice models starting from well-known lattice spin and gauge models. The challenge is to discover the correct quantum critical point in the space of these qubit models where the desired continuum quantum field theory emerges. We provide evidence of a quantum critical point where the asymptotic freedom of the 1+1-dimensional O(3) spin model emerges with just two qubits on each spatial lattice site. We also discover a continuum massive quantum field theory in a Z2 lattice gauge theory in 1+1 dimensions coupled to fermions with a single local qubit at sites and links. Finally, we propose a simple qubit regularization for SU(N) lattice gauge theories. |