##### Workshop

#### Breakdown Of Ergodicity In Isolated Quantum Systems: From Glassiness To Localization

**May 20, 2019 - Jul 12, 2019**

**Abstract**

This workshop aims to investigate the fundamental role of quantum effects in suppressing or slowing down equilibration in large systems. Tunneling and localization play a central role in shaping the dynamics of systems ranging from spin and structural glasses to quantum simulators and lattice gauge theories. In particular, many-body localization has recently emerged as a fundamentally new mechanism by which isolated quantum systems may evade equilibration even at very high temperature. The workshop will bring together researchers at the intersection of all these fields in order to stimulate the rapid development and cross-fertilization of these ideas.

**Topics**

- Many-body quantum systems: thermalization and non-equilibrium.

- Disordered systems: classical and quantum spin glasses.

- Statistical mechanics and quantum computation.

**Organizers**

B. Altshuler (Columbia University) V. Kravtsov (Landau Institute, Moscow and ICTP) C. Laumann (Boston University) G. Parisi (La Sapienza Universita' di Roma and INFN) A. Scardicchio (ICTP and INFN)

**Local organizer**

Filippo Colomo (INFN Firenze)

**Contact**

ascardic@ictp.it

claumann@bu.edu

**Related events**

Ergodicity breaking in Quantum Physics (Conference) - Jun 03, 2019

Glassy aspects of classical and quantum computation (Focus Week) - Jul 01, 2019

**Schedule**20/5-25/5: 1st Week

27/5-31/5 2nd Week

3/6-7/6 Conference

10/6-15/6: 4th Week

17/6-22/6: 5th Week

24/6-28/6: 6st Week

1/7-5/7: Focus week

8/7-13/7: 8th and last week

**Talks**

May 20, 2019 - 14:00-15:00 | Antonello Scardicchio, Chris Laumann | First Meeting for the Workshop | Introduction | |||||

May 21, 2019 - 11:30-13:00 | PXP integrability | Discussion | ||||||

May 22, 2019 - 11:00-12:30 | A.Chandran and A.Scardicchio | On recent results on the spectral form factor of localizable spin chains | Discussion | We will discuss the new results by Prosen's group which would lead to the interpretation of the MBL transition in some spin chains as a crossover. | ||||

May 23, 2019 - 11:30-13:00 | Michael Kastner | Equilibration timescales of isolated quantum systems and the role of locality | Lecture | Over the past decade or two, conditions under which a sufficiently complex isolated quantum mechanical system approaches equilibrium have been firmly established. However, for explaining why equilibration is so ubiquitously observed in nature, one needs to show not only that equilibration takes place, but also that it happens on a physically realistic timescale, neither too long for equilibrium ever to be attained, nor too short for the equilibration process to be observed. Locality is believed to be an important ingredient in order to predict physically realistic timescales. In this talk I study equilibration of an isolated quantum system by mapping it onto a network of classical oscillators in Hilbert space. By choosing a suitable basis for this mapping, the degree of locality of the quantum system reflects in the sparseness of the network. I present a Lieb-Robinson bound on the speed of propagation across the classical network, from which an estimate of the equilibration timescale of the quantum system is obtained. The more local the Hamiltonian and observables, the longer the equilibration timescale predicted by the bound. The results are confirmed by exact diagonalisation for small system sizes, where estimated equilibration times are not only found to lower-bound the numerically obtained equilibration times, but also to qualitatively capture their functional dependencies. | ||||

May 27, 2019 - 12:00-12:30 | Organizers | Start of the week meeting | Discussion | Weekly meeting to present the new arrivals and discuss some organizational issues | ||||

May 28, 2019 - 11:30-13:00 | R.Moessner | The surprising usefulness of spin waves | Lecture | TBA | ||||

May 29, 2019 - 11:30-13:00 | M. Fabrizio | Twisted Bilayer Graphene | Lecture | I will briefly introduce the physics of twisted bilayer graphene at small magic angles, a group analysis of the band structure and some recent results from our group. Refs.: https://arxiv.org/pdf/1904.06301.pdf https://arxiv.org/pdf/1809.11140.pdf | ||||

May 30, 2019 - 11:30-13:00 | F. Ricci-Tersenghi | Ergodicity breaking in off-equilibrium dynamics of glassy mean-field models | Lecture | |||||

May 31, 2019 - 03:00-04:00 | D. Basko | Bound states and Landau-Zener physics near a singular continuum | Seminar | |||||

May 31, 2019 - 11:30-13:00 | F. Franchini | The Frustration of being Odd | Seminar | At the core of every frustrated system one can identify the existence of frustrated rings that is usually interpreted in terms of single particle physics. We challenge this point of view, by showing that the ring's entanglement entropy cannot be accounted for through a single excitation. Moreover, we are lead to question whether different boundary conditions can determine a different phase. In particular, we consider spin chains made by an odd number of sites with short-range antiferromagnetic interactions and periodic boundary conditions. While for distances of the order of the correlation length the phenomenology is similar to that of the non-frustrated case, we find that correlation functions involving a number of sites scaling like the system size follow different rules. The von Neumann entanglement entropy violates the area law, while not diverging with the system size, resulting into a new behavior, never observed before, which we determine to follow a universal law. In certain regions of parameters, the frustrated boundary conditions induce exact degeneracies for the ground states (even at finite sizes) and we can define an order parameter that characterizes a phase due to boundary conditions. While we are sure of these striking results, we would like to have a discussion on their interpretation. | ||||

Jun 10, 2019 - 12:00-12:30 | Chris Laumann | Organizational Meeting | Discussion | |||||

Jun 11, 2019 - 11:00-12:30 | D. Lidar | Overcoming errors in quantum annealing | Seminar | |||||

Jun 12, 2019 - 11:30-13:00 | M. Mueller | Coherent oscillators, spectral hole-burning and emerging q-bits in rare earth magnets | Lecture | Experiments in rare earth compounds, such as LiHoYF4 and GdGa-garnet, have demonstrated very long lived, coherent quantum degrees of freedom with sharply defined excitation energies, many orders of magnitude below the scale of typical magnetic interactions (exchange, dipolar or hyperfine interactions), and with life times on the order of seconds. The nature of these coherent entities in the midst of a crystalline environment has remained a mystery for a long time. I will discuss their likely origin and argue that they arise from an intricate interplay between several nuclear and electronic spins. The sharpness of the excitations is protected by Anderson localization with an unusual type of power law hopping. The emerging well isolated degrees of freedom may be promising candidates for magnetic qubits. If time permits, I will discuss new ideas of how to realise quantum memories and gates based on electro-nuclear qubits. | ||||

Jun 13, 2019 - 11:30-12:30 | J. Kurchan | Completing the eigenstate thermalization hypothesis (ETH) | Seminar | The ETH is richer than is usually assumed. I will present two new directions: higher point correlators (as are needed to calculate the OTOC) and probability distributions of matrix elements. Work in collaboration with Laura Foini. | ||||

Jun 14, 2019 - 11:30-12:30 | M. Filippone | Experimental observation of local relaxation in Many-Body Localized systems and the doublon mobility gap | Seminar | The presence of interactions leads to crucial differences between the dynamics of Many-Body Localized (MBL) and Anderson Localized (AL) systems. Interactions are responsible of exponentially slow dephasing between distant degrees of freedom. Crucially, slow dephasing is responsible for the logarithmic-in-time growth of entanglement for initial product states [1,2] and, at the same time, for the power law decay of temporal fluctuations of local observables [3]. As a consequence, after a quench, MBL systems relax to highly nonthermal stationary states at long times, while in AL relaxation is totally absent, even though AL does not exhibit particle diffusion as well. I will present and discuss out-of-equilibrium measurements of local observables performed on a circuit-QED 9-qubit architecture simulating the disordered Bose-Hubbard model. These measurements show qualitative difference between diffusive, AL and MBL dynamics [4]. If time permits, I will then discuss recent work [5] showing the existence of a `mobility gap' in the presence of single doublon excitations in Fermi- and Bose-Hubbard disordered systems. Or, in other words, I will discuss how a single doublon manages to thermalize a localized system. [1] Marko Žnidarič, Tomaž Prosen, and Peter Prelovšek Phys. Rev. B 77, 064426 (2008) [2] Jens H. Bardarson, Frank Pollmann, and Joel E. Moore PRL 109, 017202 (2012) [3] Maksym Serbyn, Z. Papić, and D. A. Abanin Phys. Rev. B 90, 174302 (2014) [4] B. Chiaro , C. Neill, A. Bohrdt, M. Filippone, D. A. Abanin, M. Knap, P. Roushan, J. Martinis et al., to be published [5] Ulrich Schneider, Théo Pellegrin, Piet W. Brouwer, D. A. Abanin and Michele Filippone, to be published | ||||

Jun 18, 2019 - 11:30-12:30 | I. Khaymovich | Correlation induced localization | Seminar | The standard picture of the 3d Anderson localization is known to be restored in low-dimensional systems by adding either the correlations in the diagonal disorder or long-range hopping terms. Recently, the Anderson's picture has been argued by providing counterintuitive examples of long-ranged systems with almost all localized states even in a nominally ergodic regime. These "new" models demonstrate either critical or localized wavefunction behavior with a "mysterious" duality of decay rates [1]. These systems belong to a new universality class where the localization properties are governed by hopping correlations. In my talk I provide general localization-delocalization principles [2] needed for such models to find a full phase diagram and uncover the role of correlations and the origin of the duality [1]. I present a new class of random Hamiltonians with translation-invariant hopping terms demonstrating the duality in the momentum and coordinate space. If time permits I will consider the stability of such fully-correlated long-ranged models to perturbations and their relations to constrained dynamics [3]. [1] X. Deng et al., PRL 120, 110602 (2018). [2] P. A. Nosov, I. M. Khaymovich, and V. E. Kravtsov, Phys. Rev. B 99, 104203 (2019). [3] P. A. Nosov, I. M. Khaymovich, arXiv:1904.11509 | ||||

Jun 20, 2019 - 11:30-12:30 | V. Varma | Length scales in the many-body localized phase and their spectral signatures | Seminar | |||||

Jun 21, 2019 - 11:30-12:30 | G. Shlyapnikov | Ergodic-nonergodic transitions in disordered quantum systems with long-range hops | Seminar | |||||

Jun 24, 2019 - 12:00-12:30 | C Laumann | Organizational meeting | Introduction | |||||

Jun 25, 2019 - 11:30-12:30 | I. Lerner | Quantum discord in electronic systems | Seminar | |||||

Jun 25, 2019 - 16:00-17:30 | J. Imbrie | Proving MBL 2 | Discussion | |||||

Jun 26, 2019 - 11:30-12:30 | A. Kamenev | SYK paradigm of interacting quantum matter | Seminar | I will review Sachdev-Ye-Kitaev (SYK) model, which has recently attracted attention as an illustration of the holographic duality and a model for non-Fermi liquid materials. My particular emphasis will be on the role of quantum fluctuations, which are described by the so-called Schwarzian field theory. These fluctuations lead to metal-insulator quantum phase transition with a wide "strange metal" quantum critical region. | ||||

Jun 26, 2019 - 16:00-17:30 | J. Imbrie | Proving MBL 3 | Discussion | |||||

Jun 27, 2019 - 11:30-12:30 | V. Bazhanov | On the scaling behaviour of the alternating spin chain | Seminar | |||||

Jun 27, 2019 - 14:00-15:00 | P. Cappellaro | TBA | Seminar | |||||

Jun 28, 2019 - 11:30-12:30 | M. Znidaric | Localized and ballistic eigenstates in chaotic spin ladders and the Fermi-Hubbard model | Seminar | I will introduce a class of spin ladder models that is in general chaotic, can be disordered, and includes the integrable Hubbard chain as a special case. Nevertheless, one can analytically show the existence of exponentially many atypical eigenstates that are populated by noninteracting excitations. Depending on parameters they can e.g. exhibit Anderson localization, or, surprisingly, ballistic transport at any disorder strength. These properties differ strikingly from those of typical eigenstates nearby in energy which give rise to diffusion. Results have implications for possible localization in the presence of non-Abelian symmetries, as well as for recent interest in states avoiding thermalization. | ||||

Jul 09, 2019 - 11:15-11:45 | R. Moessner | Frustrated magnets and Jamming | Talk | |||||

Sep 07, 2019 - 11:45-12:30 | L. Zhou | Sparsifying Hamiltonians | Seminar | |||||

Oct 07, 2019 - 11:30-12:30 | J. Arenas | Energy versus spin transport in disordered quantum chains | Seminar |