##### Workshop

#### Entanglement in Quantum Systems

**May, 21 2018 - Jul, 13 2018**

The event is partially supported by the Simons Collaboration "It from Qubit"

**Organizers**

*Pasquale Calabrese *(SISSA, Trieste)

*Ignacio Cirac *(Max Planck Institute, Garching)

*Joel Moore *(University of California, Berkeley)

*Robert Myers * (Perimeter Institute, Waterloo)

*Mukund Rangamani *(University of California, Davis)

*Tadashi Takayanagi *(Yukawa Institute, Kyoto)

*Erik Tonni *(SISSA, Trieste)

**Local organizer**

Domenico Seminara

**Contact**

etonni@sissa.it

seminara@fi.infn.it

**Related events**

Entanglement in Quantum Systems (Conference) - Jun, 04 2018

Quantum Information in Quantum Gravity 4 (Meeting) - Jun, 11 2018

Tensor Networks and Entanglement (Focus Week) - Jun, 18 2018

**Abstract**

Understanding the nature of entanglement in quantum systems has been an important challenge in theoretical physics since the early days of quantum mechanics. However, it is only during the last decade that entanglement became a powerful tool to characterize extended quantum systems. Various aspects of quantum entanglement have been studied by employing the most advanced methods available in Quantum Field Theory, Quantum Gravity, Condensed Matter and Quantum Information. Despite the great achievements, many important theoretical questions are still unanswered and it is nowadays evident that an interdisciplinary effort is necessary to find satisfactory solutions.

The aim of this workshop is bringing together a broad spectrum of theorists who have a strong expertise in the areas of Quantum Field Theory, Quantum Gravity, Condensed Matter Theory and Quantum Information, including also some experimentalists, in order to exchange knowledge and discuss open problems related to entanglement from different perspectives.

**Topics**

- Entanglement measures in Quantum Field Theories

- Entanglement in many-body systems

- Entanglement in Quantum Gravity: gravitational constraints and emergence of spacetime

- Role of entanglement in Quantum Information

- Tensor networks and entanglement

- Experimental detection of entanglement

**ACRI fellowships**

Individual fellowships are available for young researchers funded by ACRI under the “Young Investigator Training Program 2017”. The fellowship supports a scientific visit of at least one month in Italy: it provides 3000 euro for researchers from Europe or 4000 euro for those from outside Europe. The visit must include the attendance of the program “Entanglement in Quantum Systems” at GGI for at least two weeks. The remaining time must be spent in another research institute in Italy among the ones selected for this program, which are listed here, together with the corresponding contact person, who must approve the visit. A CV and a research statement including the chosen research institute and the reasons for this choice must be sent by email to Erik Tonni. The deadline is February 15, 2018.

**Preview**

**Poster sessions**

Poster sessions will be organised during the three events (main conference, QIQG4 meeting and tensor network focus week). The participants who would like to present a poster are kindly invited to send an email with the title and a short abstract to Erik Tonni before May 16, specifying also in which event(s) they want to make their presentation. Since a limited number of panels is available, the organisers will select the presentations shortly after the deadline. The poster panels will also be available even during the program, therefore the participants who wants to show a poster during their stay even outside the three key events are kindly invited to follow the above procedure.

**Talks**

May, 22 2018 - 15:00 | Tatsuma Nishioka | OPE for Conformal Defects and Holography | Talk | |||||

May, 23 2018 - 11:30 | Tomonori Ugajin | Relative entropy in CFT | Talk | |||||

May, 24 2018 - 15:00 | Romuald Janik | Exact Matrix Product State for the Klein-Gordon bosonic chain | Talk | |||||

May, 25 2018 - 11:30 | Djordje Radicevic | Flux-attached gauge theories and topological entanglement entropy | Talk | |||||

May, 28 2018 - 15:00 | Benjamin Doyon | Emergent hydrodynamics in integrable systems out of equilibrium | Talk | I will introduce the recently developed theory of "generalized hydrodynamics" (GHD). This describes large-scale behaviours in many-body quantum and classical integrable systems out of equilibrium - in inhomogeneous states and force fields - by adapting the principles of hydrodynamics to the presence of infinitely many conservation laws. I will then cover one or more of the following topics: how GHD can be used to describe cold atom gases in one-dimensional settings and theoretically solve the famous quantum Newton cradle experiment; how it predicts the validity of conventional hydrodynamics at zero temperature before shocks appear and prevents shock formations; how it describes classical systems such as the hard rod gas, soliton gases and the gases of classical field radiations; how it gives rise to Euler-scale correlation functions, Drude weights, and scaled cumulant generating functions (non-equilibrium current, zero-frequency noise, full counting statistics) for non-equilibrium transport; what the underlying geometry is; some GHD exact solutions and numerical techniques. | ||||

May, 29 2018 - 15:00 | Giuseppe Policastro | Holographic complexity and defect CFT | Talk | Recently the concept of complexity has been proposed by Susskind as a measure of the more subtle properties of information processing in the context of black holes physics, and a conjecture on how to measure this quantity in the holographic correspondence was put forward. It still remains to be proven, however, that the complexity can be a useful and well-defined concept in quantum field theory. I will describe this developments, then present our calculation of the complexity for a conformal field theory in presence of a defect. | ||||

May, 30 2018 - 15:00 | Paul Fendley | Baxterising using topological defects and conserved currents | Talk | Many integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess an unusual sort of conserved current, built by terminating a topological defect. Such currents have been constructed by utilising quantum-group algebras, fermionic and parafermionic operators, and ideas from ``discrete holomorphicity''. I define them generally and naturally using a braided tensor category, a structure familiar from the study of knot invariants and from conformal field theory. Requiring the existence of the currents provides a simple way of ``Baxterising'', i.e. building a solution of the Yang-Baxter equation out of topological data. This approach allows many new examples of conserved currents to be found, for example in height models. Although integrable models found by this construction are critical, I find one non-critical generalisation: requiring a ``shift'' operator in the chiral clock chain yields precisely the Hamiltonian of the integrable chiral Potts chain. | ||||

May, 31 2018 - 11:30 | David Perez Garcia | Bulk-boundary correspondence in PEPS | Talk | |||||

May, 31 2018 - 15:00 | Tommaso Roscilde | Finding entanglement in a path integral | Talk | Certifying and analyzing the entanglement content of quantum mixed states is a most important challenge for theory and experiments alike. In the absence of unambiguous entanglement estimators for mixed states, a valid alternative approach is the formulation of entanglement witnesses, aimed at detecting the non-separability and the entanglement pattern of the largest possible class of entangled density matrices. This approach has recently experienced very important advances, thanks to the discovery that quantum coherence estimators, certifying the non-diagonal nature of the quantum state on the eigenbasis of a given observables, can act as effective entanglement witnesses. In this seminar I shall discuss how fundamental information on quantum coherence can be extracted from standard tools in quantum statistical physics. Quantum coherence is encoded in the imaginary-time evolution of observables; and it can be quantified geometrically within a path-integral representation of the quantum state, by estimating the variance of imaginary-time fluctuations. Such a variance has an immediate physical meaning, as the difference between fluctuations and susceptibility of an observable. This framework offers very powerful tools for entanglement witnessing in all the models whose equilibrium statistical physics can be quantitatively reconstructed, either analytically or numerically. I shall illustrate a few applications to models in the vicinity of a quantum critical point. | ||||

Jun, 01 2018 - 15:00 | Clement Berthiere | Boundary contribution to (holographic) entanglement entropy | Talk | The entanglement entropy, while being under the spotlight of theoretical physics for more than ten years now, remains very challenging to compute, even in free quantum field theories, and a number of issues are yet to be explored. One such issues concerns boundary effects on entanglement entropy, which is important both for theoretical explorations of entanglement and for applications of entanglement entropy to lattice simulations, condensed matter systems, etc.. During this talk, I will show how the presence of spacetime boundaries affects the entanglement entropy, with emphasize on universal (boundary-induced) logarithmic terms, using field theoretic, lattice, and holographic methods. | ||||

Jun, 25 2018 - 15:00 | Jacopo Viti | Exact logarithmic boundary four-point functions in 2d critical percolation | Talk | I'll discuss how to calculate geometrical boundary four-point functions in critical percolation using conformal invariance. The results which I'll discuss provide a rare instance of logarithmic singularities in statistical mechanics. This is a joint work with Giacomo Gori. | ||||

Jun, 26 2018 - 15:00 | Simon Ross | ETH and conserved charges of 1+1 CFTs | Talk | |||||

Jun, 27 2018 - 11:00 | Maurizio Fagotti | Time evolution of the bipartite entanglement in integrable systems | Talk | We consider the dynamics of the entanglement entropies of bipartitions after global quantum quenches. We review the behavior of the entropies in noninteracting models and present a revised semiclassical theory, which turns out to be fully predictive. We discuss the generalizations to interacting systems and present new results, both in homogeneous and in inhomogeneous settings. | ||||

Jun, 27 2018 - 15:00 | Jacopo De Nardis | Bound states in integrable chains: from quantum quenches to spin and charge transport | Talk | We show how in the past few years the knowledge of the bound states in integrable models has been necessary in order to understand their non-equilbrium physics. We also show how large bound states are responsible for the anomalous transport properties (ballistic and super-diffusive transport) of many integrable chains. | ||||

Jun, 28 2018 - 11:00 | Raul Arias | Local Temperatures in Modular Hamiltonians | Talk | I will introduce the notion of Modular Hamiltonian and relating it to the relative entropy I will give a definition of local temperatures. In the second part of the talk I will show you how to compute it and some simple examples where analytic solutions were found. | ||||

Jun, 28 2018 - 15:00 | Andrei Parnachev | Regge limit in holographic CFTs | Talk | We will discuss the Regge limit of four-point functions in holographic CFTs and its applications. | ||||

Jun, 29 2018 - 11:00 | Jean-Marie Stephan | Entanglement scaling in 1d critical states (slightly) beyond the usual CFT | Talk | The entanglement entropy diverges logarithmically with subsystem size for ground states of 1+1d conformal field theories (CFT). Since most quantum critical points in 1d are described by CFT, this mild violation of the area law is often seen as a signature of quantum criticality. In this talk, I consider two classes of states that go beyond the above picture. The first allows for position-dependent couplings in the Hamiltonian, that is for example relevant to the physics of cold atom gases trapped in harmonic potentials. I will show how the CFT formalism may be adapted to handle this case also, and derive a few exact formulas. The second is constructed by gluing several copies of the euclidean CFT along some boundary. When the number of copies is large enough those provide examples of critical states whose entropy saturates to a constant for large subsystem size. | ||||

Jun, 29 2018 - 15:00 | Gabriel Wong | Glueing together Modular flows with free fermions | Talk | We revisit the calculation of multi-interval modular Hamiltonians for free fermions using a Euclidean path integral approach. We show how the multi-interval modular flow is obtained by glueing together the single interval modular flows. Our methods are based on a derivation of the non-local field theory describing the reduced density matrix, and makes manifest it's non-local conformal symmetry and $U(1)$ Kacs-Moody symmetry. We will show how the non local conformal symmetry provides a simple calculation of the entanglement entropy. | ||||

Jul, 02 2018 - 15:00 | Ingo Peschel | The entanglement Hamiltonian of free-fermion chains | Talk | |||||

Jul, 03 2018 - 15:00 | Hong Liu | Emergent entropy | Talk | In this talk we discuss a new proof of the second law of thermodynamics. For this purpose we develop a general non-equilibrium effective field theory of slow degrees of freedom from integrating out fast degrees of freedom and consider its classical limit. The key elements of the proof are the presence of a Z_2 symmetry, which can be considered as a proxy for local equilibrium and micro-time-reversibility, and a classical remnant of quantum unitarity. The Z_2 symmetry leads to a local current from a procedure analogous to that used in the Noether theorem. Unitarity leads to a definite sign of the divergence of the current. We also discuss the origin of an arrow of time, as well as the coincidence of causal and thermodynamical arrows of time. | ||||

Jul, 04 2018 - 11:00 | Dmitry Abanin | Quantum many-body scars: a new mechanism of ergodicity breaking | Talk | The thermodynamic description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. Recent studies of many-body localization have revealed the existence of systems that strongly violate ergodicity in the presence of quenched disorder. Here, we demonstrate that ergodicity can be weakly broken by a different mechanism, arising from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems. In the single-particle case, quantum scars correspond to wave functions that concentrate in the vicinity of unstable periodic classical trajectories. We show that many-body scars appear in the Fibonacci chain, a model with a constrained local Hilbert space that has been recently experimentally realized in a Rydberg-atom quantum simulator. The quantum scarred eigenstates are embedded throughout the otherwise ergodic many-body spectrum, but lead to direct experimental signatures, as we show for periodic recurrences that reproduce those observed in the experiment. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, opening up opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable. | ||||

Jul, 05 2018 - 11:00 | Roger Melko | Entanglement entropy of corners in interacting quantum field theories | Talk | |||||

Jul, 06 2018 - 11:00 | Federico Galli | Holographic second laws of black hole thermodynamics | Talk | It has been shown that for out-of-equilibrium systems there are additional constraints on thermodynamical evolution besides the ordinary second law. These form a new family of second laws of thermodynamics and are equivalent to the monotonicity of quantum Rényi divergences under transitions. In black hole thermodynamics, the usual second law is manifest as the area increase theorem. I will discuss these additional laws within the AdS/CFT correspondence as to explore whether they imply new restrictions for out-of-equilibrium black holes and possibly comment on extensions to asymptotically flat black holes. | ||||

Jul, 09 2018 - 14:30 | Andrea Cappelli | Topological Insulators in 3D and bosonization | Talk | Massless excitations at the edge of topological insulators possess both fermionic and bosonic descriptions. In two dimensions, the map between bosons and fermions is well understood within the edge conformal field theory. In three dimensions, we use effective actions and partition functions to establish some basic properties of the corresponding bosonization map. | ||||

Jul, 10 2018 - 15:00 | Vijay Balasubramanian | Statistically random coupling constants from entanglement with dark matter | Talk | |||||

Jul, 11 2018 - 11:00 | Jiaju Zhang | 1/c corrections to various quantities in a 2D large c CFT | Talk | The weakly coupled 3D gravity is dual to a 2D large c CFT. While quantum gravity is far from reach at this moment, with help of the AdS/CFT correspondence one can tackle gravity problems using CFT techniques. Classical gravity results sometimes lead to puzzles, and I will talk about how 1/c corrections in CFT can solve some of them. The cases I will talk about include mutual information of two disjoint intervals on a plane, entanglement entropy of one interval on a torus, eigenstate thermalization hypothesis, entanglement plateau, and the Holevo information. The main CFT technique is the short interval expansion from OPE of twist operators. | ||||

Jul, 12 2018 - 11:00 | Damian Galante | Centaurs and butterflies: deformations of dS-like geometries embedded in AdS | Talk | I will describe two-dimensional geometries that smoothly interpolate between an asymptotically Anti-de Sitter geometry and the static patch of de Sitter. These "centaur" geometries can be a fruitful ground to probe dS in the context of holography. I will show how these geometries change under different types of deformations and in particular, analyze their relation with the recently proposed bound on chaos. | ||||

Jul, 13 2018 - 11:00 | Francesco Bigazzi | Top-down holography and the Chern-Simons Diffusion Rate | Talk | I will show that, within a large class of planar strongly correlated gauge theories with dual string description, the Chern-Simons diffusion rate - a relevant observable for the Chiral Magnetic Effect - is simply given in terms of temperature, entropy density and gauge coupling, with a universal numerical coefficient. This result holds, in fact, for all the top-down holographic models where the calculation has been performed in the past, even in presence of magnetic fields and anisotropy. I will also point out some subtleties related to the definition of the Chern-Simons diffusion rate in the presence of anomalies. The standard Kubo formula for the rate - a late time limit of the imaginary part of the retarded correlator of the topological charge density - gives an exactly vanishing result at zero frequency. Nevertheless, a non-trivial Chern-Simons relaxation time can be safely defined in this case. |