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New perspectives on quantum many-body chaos

Discussion meeting

Overview

Online scientific discussion meeting organised by Dr Zlatko Papic, Professor Juan Garrahan, Professor Jonathan Keating FRS, Dr Mike Blake and Dr Achilleas Lazarides.

Credit: Zlatko Papic

In the last few years the study of chaos in interacting quantum many-body systems has experienced a remarkable resurgence, combining insights from mathematical physics, string theory and condensed matter physics. This timely meeting will bring together an international selection of researchers to cement the UK’s position as a world leader in this rapidly developing field.

More information on the schedule of talks and speaker biographies will be available soon. Speaker abstracts will be available closer to the meeting date. Meeting papers will be published in a future issue of Philosophical Transactions of the Royal Society A.

Attending this event

This meeting is intended for researchers in relevant fields and will take place online. Please register using the Eventbrite link above.

Poster Session

There will be an opportunity to present a poster online at this meeting. If you would to apply, please submit your proposed title, abstract (no more than 200 words and in third person), author list, name of the proposed presenter and institution to the Scientific Programmes team no later than Monday 25 January 2021. Subject line of the email should be "Poster abstract: Quantum many-body chaos". Please note that places are limited and are selected at the scientific organisers' discretion.

Enquiries: contact the Scientific Programmes team

Event organisers

Select an organiser for more information

Schedule of talks

08 February

15:00-19:00

Session 1

5 talks Show detail Hide detail

Chairs

Dr Achilleas Lazarides, Loughborough University, UK

15:00-15:40 Probing and controlling many-body dynamics in Rydberg atom arrays

Professor Mikhail Lukin, Harvard University, USA

Abstract

Controlling non-equilibrium quantum dynamics in many-body systems is an outstanding challenge as interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We experimentally investigate non-equilibrium dynamics following rapid quenches in a many-body system composed of up to   256 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we probe coherent revivals corresponding to quantum many-body scars. Remarkably, we discover that scar revivals can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating novel ways to steer entanglement dynamics in many-body systems and enabling potential applications in quantum information science.

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15:40-16:20 Localisation phenomena in frustrated magnets

Professor Claudio Castelnovo, University of Cambridge, UK

Abstract

Elementary excitations in frustrated magnetic systems often take the form of fractionalised point-like quasiparticles. In recent years significant progress was made to understand the nature of these excitations and the importance of their effective description to gain insight into the thermodynamic properties of frustrated systems. Their dynamics on the other hand remains to date a significantly taller order. Whereas in a few cases the quasiparticles can be modelled as free, their interplay with the underlying spin vacuum from which they are borne is generally highly nontrivial. The result is a rich playground of constrained motion, reduced (fractal) dimensionality, and self-generated disorder, giving rise to intriguing instances of slow dynamics and localisation which may be accessible in state of the art experiments on magnetic systems. This talk reviews some key examples, in the context of U(1) spin ice and Z_2 spin liquids, and a compass model of complex oxides. In the U(1) case, dynamical constraints lead to quasi-1D motion on random comb structures where configurational disorder produces compact localised states that survive in presence of interactions. In the Z_2 case, correlation holes induced by semionic statistics give rise to long-lived metastable states and strong out-of-equilibrium behaviour. Finally, in the compass model, disorder free localisation results in dynamical behaviour characteristic of many-body-localised system, including the logarithmic growth of entanglement; this is all the more exciting since signatures are accessible in certain components of the dynamical structure factor, experimentally measurable in the magnetic oxides described by this model. 

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16:20-16:40 Coffee break

16:40-17:20 A constructive theory of the numerically accessible many-body localized to thermal crossover

Dr Anushya Chandran, Boston University, USA

Abstract

Numerical studies generically reveal that disordered quantum chains thermalize at weak disorder, and many-body localize (MBL) at strong disorder. The crossover at intermediate disorder strengths is poorly understood as it is only accessible by exact diagonalization (ED) in short chains. Phenomenological descriptions of the MBL-thermal transition abound, but these rely on rare-region effects and thus describe the crossover at much larger chain lengths if they apply at all.

We construct a theory for the numerically observed one-dimensional MBL-thermal crossover by analysing the statistics of many-body resonances induced by local perturbations in a presumptively MBL chain. The model reproduces several properties of the crossover region, including an apparent correlation length exponent of \nu=1, the linear drift of the critical disorder strength with system size, scale-free resonances, sub-thermal entanglement entropy of small subsystems, and exponential increase of the Thouless time with disorder strength. We derive the controversial numerical observations in recent works challenging the MBL orthodoxy and argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.

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17:20-18:00 Optically Programmable Interactions for Quantum Simulation

Professor Monika Schleier-Smith, Stanford University, USA

Abstract

The dream of the quantum engineer is to have an “arbitrary waveform generator” for designing quantum states and Hamiltonians.  Motivated by this vision, I will report on advances in optical control of long-range interactions among cold atoms.  By coupling atoms to light in an optical resonator, we generate tunable non-local Heisenberg interactions, characterizing the resulting phases and dynamics by real-space imaging.  Notable observations include interaction-based protection of spin coherence and photon-mediated spin-mixing—a new mechanism for generating correlated atom pairs.  I will present recent results on optically programming the distance-dependence of the spin-spin couplings, with prospects for studies of fast scrambling.  I will also touch on broader prospects in quantum simulation, quantum optimization, and quantum metrology.

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18:00-19:00 Poster Session

09 February

15:00-19:00

Session 2

5 talks Show detail Hide detail

Chairs

Dr Zlatko Papic, University of Leeds, UK

15:00-15:40 Exact eigenstates in non-integrable systems: A violation of ETH

Professor Andrei Bernevig, Princeton University, USA

Abstract

We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. We then focus on the eta pairing states and show that they can become scars upon a Hamiltonian deformation; this gives a “generic” way of obtaining SCARS by deforming a Lie algebra.

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15:40-16:20 Many body quantum chaos and Feynman histories

Professor John Chalker, University of Oxford, UK

Abstract

We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local couplings that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are many-body orbits in Fock space. A natural simplification of these sums is the diagonal approximation, where the only terms that are retained are ones in which each orbit is paired with a partner that carries the complex conjugate weight. We examine when the diagonal approximation holds, its consequences in calculations of physical properties, and the nature of the leading corrections to it. We show that properties are dominated at long times by contributions to orbit sums in which each orbit is paired locally with a conjugate, as in the diagonal approximation, but that in large systems these dominant contributions consist of many spatial domains, with distinct local pairings in neighbouring domains. The existence of these domains is reflected in deviations of the spectral form factor from RMT predictions, and of matrix element correlations from ETH predictions; deviations of both kinds diverge with system size. We demonstrate that our physical picture of orbit-pairing domains has a precise correspondence in the spectral properties of a transfer matrix that acts in the space direction to generate the ensemble-averaged spectral form factor. (Joint work with Sam Garratt.)

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16:20-17:00 Random multipolar driving: tunably slow heating through spectral engineering

Professor Roderich Moessner, Max Planck Institute for the Physics of Complex Systems, Germany

Abstract

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the time-scale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n−multipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For n≥1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n+1. A simple theory based on Fermi's golden rule accounts for this behaviour. The quasiperiodic Thue-Morse sequence corresponds to the n→∞ limit, and accordingly exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile non-equilibrium phases, which we illustrate with a random multipolar discrete time crystal. 

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17:00-17:20 Coffee break

17:20-18:00 Presentation by Professor Eric Heller: Talk title tbc

18:00-19:00 Panel Discussion 1

Dr Maksym Serbyn, IST, Austria
Professor Lea Santos, Yeshiva University, USA
Professor Vedika Khemani, Stanford University, USA
Professor Michael Knap, Technical University of Munich, Germany

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10 February

15:00-18:30

Session 3

4 talks Show detail Hide detail

Chairs

Professor Jon Keating FRS, University of Bristol, UK

15:00-15:40 Results and new perspectives on quantum spin glasses

Professor Simone Warzel, Technical University of Munich, Germany

Abstract

Quantum spin glass models of mean-field type are prototypes of quantum systems exhibiting phase transitions related to the spread of the eigenstates in configuration space. Originally motivated by spin glass physics and as complex model systems to test quantum adiabatic algorithms, they are also discussed in relation to many-body localisation phenomena. Remarkably, despite being non-integrable quantum spin glasses are expected to possess intermediate phases in which eigenstates occupy only a fraction of configuration space.

In this talk, Professor Warzel will introduce a class of hierarchical quantum glasses for which this assertion can be proven at least on the level of the specific free energy. This class constitues the quantum version of Derrida's generalised random energy models. The quantum nature is thereby incooperated through a transversal magnetic field. By proving a quantum Parisi formula for their free energy the full phase diagram is established: the model exhibits spin glass phases as well as mixed and quantum paramegnetic phases. 

The mechanism behind this is the principle of erasure of hierarchical spin glass order: types of spins decide in groups whether to freeze into quantum paramagnetic order or not depending on the strength of the transversal magnetic field and the temperature. 

I will conclude the talk with an overview of conjectures related to the fate of Parisi's order parameter and the structure of the eigenfunctions for these models. 

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15:40-16:20 Spectral statistics of chaotic many-body systems

Dr Sebastian Müller, University of Bristol, UK

Abstract

We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. (Joint work with Rémy Dubertrand)

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16:20-17:00 The Eigenstate Thermalization Hypothesis: What is it, and what can be proved?

Steve Zelditch, Northwestern University, USA

Abstract

The ETH conjectures that  in the large N mean field limit, certain  N-particle quantum systems are quantum ergodic in roughly the same sense as in known results for  single particle quantum systems whose classical limit is ergodic. The ETH has been studied in many physics articles, but the only rigorous mathematical results to date appear to be in random matrix theory, and in a quite different spirit  from semi-classical quantum ergodicity. My talk will first review the definition of ETH from  some of the well-known physics articles and review the models which they believe to satisfy the ETH. Then I review the known mathematical  results in many body quantum mechanics concerning the mean field (classical) limit  of many body systems, in particular  Egorov theorems  (due to Ammari-Nier, Frohlich-Knowles and others).  Finally, I review the standard results on quantum ergodicity and mixing, including converse results which say that the classical limit must be mixing if the ETH holds for it.   

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17:00-17:30 Coffee break

17:30-18:30 Panel Discussion 2

Professor Tomaz Prosen, University of Ljubljana, Slovenia
Professor Paul Fendley, Oxford University, UK
Professor Ehud Altman, University of California Berkeley, USA
Professor Andrew G Green, University College London, UK

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11 February

15:00-18:30

Session 4

4 talks Show detail Hide detail

Chairs

Dr Mike Blake, University of Bristol, UK

15:00-15:40 Spectral properties and thermalization with matrix product states

Dr Mari-Carmen Banuls, Max Planck Institute of Quantum Optics, Germany

Abstract

Matrix product states, and operators, are powerful tools for the description of low energy eigenstates and thermal equilibrium states of quantum many-body systems in one spatial dimension. But in out-of-equilibrium scenarios, and for high energy eigenstates of generic systems, the scaling of entanglement with time and system size makes a direct application often impossible. However, beyond the standard algorithms, MPS and more general TNS techniques can still be used to explore some of the most interesting dynamical properties.

A particular case is a recently introduced method in which MPO techniques are combined with Chebyshev polynomial expansions to explore spectral properties of quantum many-body Hamiltonians. In particular, this method can be used to probe thermalization of large spin chains without explicitly simulating their time evolution, as well as to compute full and local densities of states.

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15:40-16:20 Hydrodynamics and the Spectral Form Factor

Professor Brian Swingle, Brandeis University, USA

Abstract

Ensembles of quantum chaotic systems are expected to exhibit random matrix universality in their energy spectrum. The presence of this universality can be diagnosed by looking for a linear in time 'ramp' in the spectral form factor, but for realistic systems this feature is typically only visible after a sufficiently long time. It is important to understand the emergence of this universality and how it connects to the larger body of phenomena associated with quantum chaos. This talk will present a hydrodynamic theory of the spectral form factor in systems with slow modes. The formalism predicts the linear ramp at sufficiently late time and gives a quantitative framework for computing the approach to ramp.

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16:20-17:00 Quantum Algorithmic Measurement

Professor Xiao-Liang Qi, Stanford University, USA

Abstract

Can quantum computational tools enhance the precision and efficiency of physical experiments? Promising examples are known, but a systematic treatment and comprehensive framework are missing. We introduce Quantum Algorithmic Measurements (QUALMs) to enable the study of quantum measurements and experiments from the perspective of computational complexity and communication complexity. The measurement process is described, in its utmost generality, by a many-round quantum interaction protocol between the experimental system and a full-fledged quantum computer. The QUALM complexity is quantified by the number of elementary operations performed by the quantum computer, including its coupling to the experimental system. 

We study how the QUALM complexity depends on the type of allowed access the quantum computer has to the experimental system: coherent, incoherent, etc. We provide the first example of a measurement "task", which can be motivated by the study of Floquet systems, for which the coherent access QUALM complexity is exponentially better than the incoherent one, even if the latter is adaptive; this implies that using entanglement between different systems in experiments, as well as coherence between probes to the physical system at different times, may lead to exponential savings in resources. We extend our results to derive a similar exponential advantage for another physically motivated measurement task which determines the symmetry class of the time evolution operator for a quantum many-body system. 

Many open questions are raised towards better understanding how quantum computational tools can be applied in experimental physics. A major question is whether an exponential advantage in QUALM complexity can be achieved in the NISQ era.

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17:00-17:30 Coffee break

17:30-18:30 Panel Discussion 3

Dr Ulrich Schneider, University of Cambridge, UK
Professor Monika Aidelsburger, Ludwig-Maximilians-Universität (LMU) München & Munich Center for Quantum Science and Technology (MCQST), Germany
Professor Igor Lesanovsky, University of Tübingen, Germany
Dr Norman Yao, UC Berkeley, USA

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