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Breakdown of ergodicity in quantum systems: from solids to synthetic matter

Scientific meeting

Location

The Royal Society, London, 6-9 Carlton House Terrace, London, SW1Y 5AG

Overview

Scientific discussion meeting organised by Professor Sir Michael Pepper FREng FRS, Dr Arijeet Pal, Dr Zlatko Papic, Dr Ulrich Schneider and Professor Steven Simon

A network of interacting qubits forming a quantum glass. Credit: Dr Zlatko Papic

Ergodic systems lie at the heart of statistical physics since they reach thermal equilibrium and 'forget' their initial conditions, thereby allowing for coarse-grained classical descriptions. Recently, non-ergodic quantum many-body systems, which fail to thermalise and decohere completely, came into focus. This interdisciplinary meeting addressed their fundamental challenges and experimental realisations, including many-body localisation and other novel, non-classical long-time behaviour.

The programme, speaker abstracts, and biographies of the organisers and speakers is available below. Recorded audio of the talks are also available below. Meeting papers will be published in a future version of Philosophical Transaction A.

This meeting was followed by a related satellite meeting 'Future directions in non-ergodic dynamics in quantum systems' at the Royal Society at Chicheley Hall on 8-9 February 2017.

Enquiries: Contact the Scientific Programmes team

Event organisers

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Schedule of talks

06 February

09:00-12:55

Session 1

4 talks Show detail Hide detail

Chairs

Professor Dan Shahar, Weizmann Institute, Israel

09:05-09:55 Many-body localization: answers and questions

Professor John Imbrie, University of Virginia, USA

Abstract

In considering the phenomenon of localization in isolated many-body quantum systems, it is important to get past perturbative analysis, as rare regions with weak disorder (Griffiths regions) have the potential to spoil localization. In his talk, John describes a non-perturbative construction of local integrals of motion (LIOMs) for a weakly interacting spin chain in one dimension. This leads to a proof that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a Kolmogorov-Arnold-Moser-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor-product basis into a complete set of exact many-body eigenfunctions. John discusses prospects for the level-statistics problem by reviewing recent work elucidating the way randomness localizes eigenfunctions, smooths out eigenvalue distributions, and produces eigenvalue separation.

The construction breaks down in higher dimensions, as one can no longer ensure that interactions involving the Griffiths regions are much smaller than the typical energy-level spacing for such regions. Is this an artefact of the method or is there a real barrier to exact many-body localization in dimensions 2 or more? 

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09:55-10:45 Probing many-body localisation from an ultracold atom perspective

Professor Immanuel Bloch, Ludwig-Maximilians-Universität & Max Planck Institute of Quantum Optics, Munich, Germany

Abstract

A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalise under their own dynamics. Recently, the emergence of many-body localised (MBL) systems has questioned this concept, challenging our understanding of the connection between statistical physics and quantum mechanics. In his talk, Immanuel reports on several recent experiments carried out in his group on the observation of Many-Body Localisation in different scenarios, ranging from 1D fermionic quantum gas mixtures in driven and undriven Aubry-André type disorder potentials and 2D systems of interacting bosons in 2D random potentials. It is shown that the memory of the system on its initial non-equilibrium state can serve as a useful indicator for a non-ergodic, MBL phase. Furthermore, he will present new results on the slow relaxation dynamics in the ergodic phase below the MBL transition, where he finds evidence for Griffith’s type slow dynamics.

His group’s experiments represent a demonstration and in-depth characterisation of many-body localisation, often in regimes not accessible with state-of-the-art simulations on classical computers.

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10:45-11:15 Coffee break

11:15-12:05 Many body localization and glassiness in disordered quantum systems

Professor Antonello Scardicchio, International Centre for Theoretical Physics, Italy

Abstract

Antonello discusses the interplay of two phenomena arising in disordered quantum spin systems: the appearance of a glassy phase, and the complete suppression of transport due to many-body localization. He will review work done (analytical and numerical) on some models, under various approximations, and try to sketch a universal physical picture for how the two dynamical phases interplay. Antonello will also comment on the implications of this picture for the performance of quantum computers and in particular those implementing the quantum adiabatic algorithm.

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12:05-12:55 Exploring quantum phase slips in 1D bosonic systems

Dr Chiara D'Errico, Istituto Nazionale di Ottica - CNR and LENS, Italy

Abstract

Quantum phase slips, i.e., the primary excitations in one-dimensional superfluids at low temperature, have been well characterized in most condensed-matter systems, with the notable exception of ultracold quantum gases. Chiara presents the experimental investigation of the dissipation in one-dimensional Bose superfluids flowing along a periodic potential, which show signatures of the presence of quantum phase slips. In particular, by controlling the velocity of the superfluid and the interaction between the bosons, the D’Errico group are able to drive a crossover from a regime of thermal phase slips into a regime of quantum phase slips. Achieving a good control of quantum phase slips in ultracold quantum gases requires to keep under control other phenomena such as the breaking of superfluidity at the critical velocity or the appearance of a Mott insulator in the strongly correlated regime. Chiara presents the group’s current results in these directions.

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12:55-14:30

Lunch

14:30-16:45

Session 2

3 talks Show detail Hide detail

Chairs

Professor Mikhail Lukin, Harvard University, USA

14:30-15:20 The effect of non-Abelian symmetries on many-body localization and thermalization

Professor Dmitry Abanin, University of Geneva, Switzerland

Abstract

Many-body localization (MBL) provides the only known robust mechanism to break ergodicity and avoid thermalization in quantum many-body systems. Many-body localized systems are characterized by emergent local integrability and low, area-law entanglement of excited eigenstates. It is well-known that symmetries of the system modify single-particle, Anderson localization in non-trivial ways. Do symmetries have a significant effect on MBL and thermalization in many-body systems? In this talk, Abanin will focus on disordered systems with continuous, non-Abelian symmetries, one example being the random Heisenberg model, which has SU(2) symmetry. The symmetry dictates that the system cannot have a complete set of local integrals of motion, and therefore cannot be MBL in the conventional sense. Abanin will describe a potential non-ergodic phase, which is consistent with the symmetry. In this phase, the eigenstates have sub-thermal, logarithmic scaling of entanglement with the system size. Abanin will introduce a method for probing the stability of non-ergodic many-body phases, and apply it to the SU(2)-symmetric case, finding that the non-ergodic phase becomes unstable due to proliferation of multi-spin resonances. Such processes are missed by other approaches, such as strong-disorder renormalization group, but are crucial for thermalization in these systems. He will discuss the case of discrete non-Abelian groups, and will speculate about the possibility of ergodicity-breaking phases beyond conventional many-body localization.

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15:20-16:10 Properties of disordered systems away from localization

Dr Marko Znidaric, University of Ljubljana, Slovenia

Abstract

An important point in characterizing a given phase, for instance a many-body localized one, is to understand how it arises from neighbouring phases and how it breaks down under external influence. Znidaric will discuss three different ways of failing to be localized: an insufficient disorder strength, disorder with symmetries, and coupling to Markovian environment. If disorder is too small transport properties can be very rich, ranging from subdiffusion to superdiffusion. If disorder is strong but has symmetries, an example being the Hubbard model with charge disorder realized in experiments, the system also fails to be fully localized. Finally Znidaric will briefly mention classical-like break down of localization due to coupling to environment.

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16:10-16:40 Tea break

16:40-16:30 Small baths in many-body localization

Dr Anushya Chandran, Boston University, USA

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16:45-18:30

Poster session

07 February

09:00-12:00

Session 3

3 talks Show detail Hide detail

09:00-09:50 Consequences of MBL-type and Yang-Baxter-type integrability for observable quantum dynamics

Professor Joel Moore, University of California, Berkeley, USA

Abstract

The easiest systems in which to understand failures of ordinary thermalization are those in which there exists an infinite set of independent conserved quantities. This includes many-body localized systems, at least in one spatial dimension, and also integrable systems of Yang-Baxter type. This talk discusses consequences of the conserved quantities in both cases, with a focus on finding unconventional hydrodynamical descriptions for time evolution from various initial conditions. In the Yang-Baxter case, there are a few examples of interacting spinless fermions in which exact results are possible via integrability even far from equilibrium, and there are proposals that essentially all of the long-time dynamics may be captured in an effectively classical description.

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09:50-10:40 Non-thermalization in trapped atomic ion spin chains

Dr Paul Hess, Joint Quantum Institute and University of Maryland, USA

Abstract

Trapped atomic ions are a versatile platform for realizing interacting quantum spin models and studing quantum nonequilibrium phenomena. When spin-dependent optical dipole forces are applied to a collection of trapped ions, an effective long-range quantum magnetic interaction arises, with the potential for reconfigurable and tunable graphs. Early experiments displayed equilibrium properties of transverse Ising models with up to 25 trapped ion spins along with spectroscopic studies of excited states and quench dynamics. In this talk, Dr Hess will discuss recent studies of many-body non-thermalization processes in this system, including a different form of prethermalization and an observation of many body localization (MBL) with a programmbly disorderd Hamiltonian. Finally, by applying a periodically driven Floquet Hamiltonian tempered with a MBL Hamiltonian, he will discuss the observation of a discrete time crystal, characterized by the stable appearance of a subharmonic response of the system to the drive.

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10:40-11:10 Coffee break

11:10-12:00 Many-body localization: entanglement and efficient simulations

Professor Frank Pollmann, Technical University Munich, Germany

Abstract

Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. The entanglement turns out to be a very useful concept to study the nature of the MBL phase: it helps to form a conceptual understanding and guides the development of new numerical tools. First, Pollmann discusses how the dynamics of entanglement and mutual information help to characterize the MBL phase. Second, he will introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited low-entanglement eigenstates of MBL systems to machine precision accuracy at moderate to large disorder. This DMRG-X method explicitly takes advantage of the local spatial structure and the low entanglement which is characteristic for MBL eigenstates.

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12:00-13:30

Lunch

13:30-17:00

Session 4

3 talks Show detail Hide detail

Chairs

Professor Ehud Altman, University of California Berkeley, USA

13:00-14:20 Quantum dynamics in disordered dipolar systems

Professor Mikhail Lukin, Harvard University, USA

Abstract

Mikhail will describe two recent experiments aimed at exploring new phases in quantum dynamics of strongly interacting systems away from equilibrium. The first involves slow, critical thermalization of disordered, dipolar spin systems in black diamond. This system is used for observation of discreet time crystals in a periodically driven ensemble of a million strongly interacting electronic spins. Mikhail also reports on observation of novel types of correlations and crystalline order formed in quantum dynamics of ultra-cold atomic arrays that are assembled atom-by-atom and entangled via excitation into the Rydberg states.

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14:20-15:05 Quantum disentangled liquid states and the half filled Hubbard model

Professor Fabian Essler, Oxford University, UK

Abstract

Eigenstates at finite energy densities in integrable models are not necessarily thermal. This permits the realization of exotic states of matter as stationary states after quantum quenches. Essler will consider the question whether the recently proposed “quantum disentangled liquid”, in which thermalized and non-thermalized degrees of freedom are postulated to co-exist in finite energy density eigenstates, could be realized in strong coupling limits of integrable and possibly even non-integrable models. Essler will focus on the half-filled Hubbard model with strong repulsive interactions.

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15:05-15:35 Tea break

15:35-16:25 Dynamical manifestations of the loss of ergodicity in many-body quantum systems

Professor Lea Santos, Yeshiva University, USA

Abstract

Results are presented for the short- and long-time dynamics of isolated many-body quantum systems with two-body interactions. The decay of the survival probability at short times can be very fast, even faster than exponential when the system is strongly perturbed out of equilibrium. At long times, however, the evolution of any quantum system with a bounded spectrum slows down and shows a power-law decay. This occurs for integrable, chaotic, interacting, non-interacting, disordered, and clean systems. The value of the power-law exponent reflects the properties of the spectrum, the structure of the initial state, and the number of particles that interact simultaneously. An exponent greater than or equal to 2 occurs when the energy distribution of the initial state is ergodically filled, which guarantees thermalization. Exponents smaller than 1 indicate lack of ergodicity. The transition from the ergodic to the nonergodic phase is also manifested in the disappearance of the correlation hole, which refers to a dip of the survival probability below the saturation point. Overall, the survival probability provides more information about the system than the von Neumann entanglement entropy or the Shannon information entropy.

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Related events

Breakdown of ergodicity in quantum systems: from solids to synthetic matter The Royal Society, London 6-9 Carlton House Terrace London SW1Y 5AG UK