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Future directions in non-ergodic dynamics in quantum systems

Scientific meeting


Kavli Royal Society Centre, Chicheley Hall, Newport Pagnell, Buckinghamshire, MK16 9JJ


Satellite 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

The instances where an isolated system fails to reach thermal equilibrium raise interesting fundamental open questions. It requires new conceptual and theoretical frameworks, and novel experimental probes to describe and predict phenomena involving many quantum particles. The satellite meeting will aim to define the relevant approaches for describing transitions from thermal to non-ergodic phases of matter and their possible implications.

The programme, talk abstracts and biographies of the speakers and organisers is available below. Recorded audio of the presentations are also available below.

Prior to this meeting there was a related discussion meeting 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter' held at the Royal Society, London on 6-7 February 2017.

Enquiries: Contact the Scientific Programmes team

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Schedule of talks

08 February


Session 1

5 talks Show detail Hide detail


Professor John Imbrie, University of Virginia, USA

09:05-09:55 Evidence for a finite temperature transition to an insulating state in localized superconductors

Professor Dan Shahar, Weizmann Institute, Israel


Dan has been studying the insulating state bordering with superconductivity in disordered indium-oxide. The transport properties of this insulator indicate that it is rather unusual. In his talk, Dan will describe recent results obtained from noise and non-linear current-voltage measurements, and Ohmic transport at very low temperatures. Findings associate them with non-ergodic properties of this insulator.

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09:55-10:45 Stablity and instablity of MBL with respect to ergodic grains

Dr Wojciech de Roeck, University of Leuven, Belgium


De Roeck will describe his group’s recent work on stability of MBL when connected to small baths (ergodic grains). The talk will start from a microscopic theory that is built entirely upon the MBL/ETH dichotomy. This theory predicts in particular that it is possible for a small bath to delocalize an arbitrarily large volume of LIOM's, provided that the latter are coupled to the bath with coupling constants that decay too slowly (slower than a critical exponential rate). The theory is being tested now and it seems to be in excellent agreement with numerics. Then, De Roeck will use it to construct an RG picture of the MBL-to-ergodic transition. The presentation obtains discontinuous behaviour of the entranglement entropy and several length scales, whereas his work also identifies explicitly some divergent length scales. This is based on joint works with F Huveneers, D Luitz, M Mueller and T Thiery.

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10:45-11:15 Coffee break

11:15-12:05 Ergodicity breaking in clean, kicked quantum spin chains

Professor Tomaž Prosen, University of Ljubljana, Slovenia


Prosen will discuss numerical results and some analytic arguments supporting ergodicity breaking, or super-exponential (in inverse coupling strength) relaxation times, in clean kicked non-integrable quantum spin 1/2 chains. A class of such models can be described as quantum cellular automata for which ergodicity breaking can be conveniently characterised by analysing the leading eigenvalue of a dynamical transfer matrix in the space of translationally invariant operators.

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12:05-12:55 Glassy aspects of quantum non-ergodicity

Professor Juan Garrahan, University of Nottingham, UK


Garrahan will consider the applicability of concepts from classical soft matter physics to problems of slow relaxation and non-ergodicity in quantum many-body systems. Soft materials which display slow cooperative relaxation such as glasses often do so as a consequence, not of quenched disorder, but of effective constraints in their dynamics. These give rise to metastability, spatially fluctuating cooperative relaxation and eventual arrest. Garrahan will discuss how these ideas may connect to many-body localisation in the absence of disorder and to the fate of MBL in the presence of dissipation. He will also try to cover relations between quantum Fisher information, multipartite entanglement and measures of coherence in problems with particle conservation, which should allow to probe entanglement dynamics in both closed and open systems from the measurement of specific observables.

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Session 2

3 talks Show detail Hide detail


Professor Joel Moore, University of California, Berkeley, USA

14:30-14:45 4 Contributed talks selected from abstracts

16:10-16:45 Tea break

16:45-17:45 Panel discussion

09 February


Session 3

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Professor Antonello Scardicchio, International Centre for Theoretical Physics, Italy

09:00-09:50 Long coherence times for edge spins

Professor Paul Fendley, Oxford University, UK


Robust edge zero modes guaranteeing ground-state degeneracy are common in a topological phase of matter. A more dramatic effect occurs in the Ising/Majorana/Kitaev chain: “strong” edge zero modes result in identical spectra in the entire even and odd fermion-number sectors, up to exponentially small finite-size corrections. A strong zero mode in a clean system is not a free-fermionic fluke. In the XYZ chain/coupled Majorana wires, its presence guarantees infinite coherence time for the edge spin, even with an infinite-temperature initial state. In non-integrable systems like the Ising chain with four-fermion interactions, an “almost” strong zero mode results in a very long coherence time, falling off very slowly with system size.

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09:50-10:40 Computing quantum thermalization dynamics with tensor networks: from quantum chaos to emergent hydrodynamics

Professor Ehud Altman, University of California Berkeley, USA


The long time dynamics of generic strongly interacting quantum systems presents a fundamental challenge for theory and computation. Matrix product states, useful for describing quantum ground states, are commonly thought to be inadequate for description of dynamics. The main obstruction is the linear growth of the entanglement entropy in time, which implies exponential growth of the required matrix sizes. In his talk Altman will discuss a new approach to overcome this obstruction and accurately describe the chaotic dynamics and emergent hydrodynamic behaviour at long times using matrix product states. The key idea is that local observables thermalize quickly when subject to generic evolution and consequently follow effective classical hydrodynamics. This suggests that the entanglement growth can be truncated after the local equilibration time without sacrificing information about local observables. Our scheme for implementing this truncation is based on the time dependent variational principle, which ensures that the approximate dynamics respects all conservation laws and can be systematically improved by increasing the bond dimension. Altman will present results for thus obtained transport coefficients and chaos characteristics in the Ising model subject to both transverse and longitudinal fields.

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10:40-11:10 Coffee break

11:10-12:00 Dissipative dynamics in ultracold atoms

Professor Corinna Kollath, University of Bonn, Germany


Atomic gases cooled to Nanokelvin temperatures are a new exciting tool to study a broad range of quantum phenomena. In particular, an outstanding and rapid control over the fundamental parameters, such as interaction strength, spin composition, and dimensionality allows to realize and observe many different situations far from equilibrium. Long-standing questions such as the coupling to an environment can be investigated. In her talk, Kollath will address the question of the influence of a coupling to an environment on the system dynamics in bosonic optical lattice gases. The interplay between the interaction, the kinetic energy and the coupling to the environment causes a critical dynamics with algebraic decaying observable or a glass-like dynamics. Also the propagation of correlations will be discussed.

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Session 4

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Professor Lea Santos, Yeshiva University, USA

13:30-14:20 Non-equilibrium dynamics of atomic gases in optical cavities

Professor Nigel Cooper, University of Cambridge, UK


A novel feature of cold gases is the possibility to couple the motional dynamics of a quantum many body system to (one or more) quantized bosonic modes, describing the light fields in optical cavities. Such matter-light coupled systems show interesting forms of collective dynamics. They are subject to dissipation through fluctuations/damping of the cavity mode.  Cooper will present theoretical results that demonstrate examples of these novel collective dynamics, both in uniform and disordered settings, focusing on the question of whether or not the dissipative dynamics drive the system to a unique steady state.

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14:20-15:10 Optically driven strongly correlated quantum systems

Professor Dieter Jaksch, University of Oxford, UK


Recent experiments [1,2] indicate that selective optical driving of phonons may generate or enhance ordered phases in strongly correlated quantum materials. In his talk Jaksch will discuss quantum optically inspired models that may help explain and engineer such phenomena. Specifically, Jaksch will consider a driven fermionic Hubbard model in the strongly correlated limit where the onsite interaction dominates over the kinetic energy [3]. The driving is modelled as an alternating periodic modulation of the lattice site energy offsets. He will demonstrate how this modulation suppresses tunnelling and induces exchange interactions. The combination of these effects changes the nature of the system into an attractive Luttinger liquid and leads to enhanced fermion pairing in one spatial dimension. Jaksch will present results at zero and finite temperatures and discuss the prospect of observing driven out-of-equilibrium superconductivity in this model system.

  1. D. Fausti, R.I. Tobey, N. Dean, S. Kaiser, A. Dienst, M.C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Light-Induced Superconductivity in a Stripe-Ordered Cuprate. Science 331, 189 (2011).
  2. M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Ricco, S.R. Clark, D. Jaksch and A. Cavalleri, Possible light-induced superconductivity in K3C60 at high temperature. Nature 530, 461-464 (2016). 
  3. J. Coulthard, S.R. Clark, S. Al-Assam, A. Cavalleri and D. Jaksch, Enhancement of super-exchange pairing in the periodically-driven Hubbard model, arXiv:1608.03964 (2016).

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15:10-15:40 Tea break

15:40-16:30 Signature of non-ergodicity in low-lying excitations of disordered many-particle systems

Professor Richard Berkovits, Bar-Ilan University, Israel


The statistical properties of the entanglement spectrum of a disordered many-particle system are studied, in order to identify the localized to extended transition as function of interaction strength and excitation energy expected from the many-body localization transition. In his talk, Berkovits shows that an indication of such a transition is indeed observed, and some of the features may be interpreted as a signature of non-ergodic behaviour.

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16:30-17:05 Engineered dissipation and out-of-equilibrium many-body dynamics with cold atoms

Professor Andrew Daley, University of Strathclyde, UK


The time-dependent microscopic control available in experiments with systems of ultracold atoms has opened new opportunities to explore many-body dynamics, addressing fundamental questions both in and out of equilibrium. This control can also be extended beyond the coherent dynamics of the system, as in typical experimental regimes the dominant mechanisms for dissipation can both be described microscopically from first principles, and can be controlled with external fields. Such control originates in the separation of timescales for coupling to a reservoir and for the relaxation of the reservoir, which is typical in quantum optics. This allows us to calculate and explore the effect of dissipation on the many-body dynamics, including on the ergodicity of dynamics after a parameter quench. We can also go further, especially in engineering dissipative processes that will drive the system into specific interacting many-body states. Daley will discuss his group’s recent work in this direction, especially looking at the microscopic description of dissipation for cold atoms in optical lattices in the presence of light scattering or with the addition of a second species that acts as a reservoir, and describe applications towards the generation of strongly correlated many-body states, and the investigation of out-of-equilibrium dynamics (including in systems exhibiting many-body-localisation).

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Future directions in non-ergodic dynamics in quantum systems Kavli Royal Society Centre, Chicheley Hall Newport Pagnell Buckinghamshire MK16 9JJ