# Quantum Many-Body Dynamics

Conference Date:
Monday, May 12, 2014 (All day) to Friday, May 16, 2014 (All day)
Pirsa Collection:
Scientific Areas:
Condensed Matter
Particle Physics
Quantum Information

Scientific Areas:

Condensed Matter
Quantum Information
High Energy Physics

In recent years, much progress was achieved in realizing highly controlled and coherent many-body systems. Examples of such systems include systems of ultra-cold atoms, molecules, systems of NV-centers in diamond, and superconductiong quibits. These remarkable experimentally advances pose a conceptually new set of theoretical questions regarding the universal laws describing the evolution and relaxation of closed many-body systems. This workshop will cover the most exciting recent theoretical developments in non-equilibrium many-body physics. Focus topics include thermalization in integrable and non-integrable strongly interacting systems, thermalization breakdown, perodically driven systems, and many-body localization in systems with quenched disorder. We will discuss key changes in the field and identify the possible roles to their solution.

To register for this event, click here.

Ehud Altman, Weizmann Institute of Science
Jean-Sebastian Caux, University of Amsterdam
Luca D'Alessio, Boston University
Eugene Demler, Harvard University
Jens Eisert, Freie University Berlin
Fabian Essler, University of Oxford
Matthew Fisher, University of California, Santa Barbara
John Imbrie, University of Virginia
Robert Konik, Brookhaven National Laboratory
Aditi Mitra, New York University
Arijeet Pal, Harvard University
Anatoli Polkovnikov, Boston University
Marcos Rigol, Pennsylvania State University
Lea Santos, Yeshiva University
Antonello Scardicchio, Princeton University

Alessandro Silva, University of Trieste
Ronen Vosk, Weizmann Institute of Science

• Dmitry Abanin, Perimeter Institute
• Ehud Altman, Weizmann Institute of Science
• Oleg Boulanov, Laval University
• Michael Brockmann, University of Amsterdam
• Jean-Sebastien Caux, University of Amsterdam
• Juan Carrasquilla, Perimeter Institute
• Anushya Chandran, Perimeter Institute
• Eugene Demler, Harvard University
• Jens Eisert, Freie University Berlin
• Fabian Essler, University of Oxford
• Matthew Fisher, University of California, Santa Barbara
• Yimin Ge, Perimeter Institute
• John Imbrie, University of Virginia
• Isaac Kim, Perimeter Institute
• Robert Konik, Brookhaven National Laboratory
• William Witczak-Krempa, Perimeter Institute
• Oliver Landon-Cardinal, California Institute of Technolog
• Keith Lee, Perimeter Institute
• Ipsita Mandal, Perimeter Institute
• Aditi Mitra, New York University
• Khadijeh Najafi, Georgetown University
• Arijeet Pal, Harvard University
• Zlatko Papic, Perimeter Institute
• Anatoli Polkovnikov, Boston University
• Marcos Rigol, Pennsylvania State University
• Subir Sachdev, Harvard University
• Lea Santos, Yeshiva University
• Luiz Santos, Perimeter Institute
Antonello Scardicchio, Princeton University
• Maksym Serbyn, Massachusetts Institute of Technology
• Alessandro Silva, University of Trieste
• Miles Stoudenmire, Perimeter Institute
• Jonathan Torres-Herrera, Yeshiva University
• Guifre Vidal, Perimeter Institute
• Ronen Vosk, Weizmann Institute of Science

Monday, May 12th, 2014

 Time Event Location 8:30 – 9:00am Registration Reception 9:00 – 9:05am Welcome and Opening Remarks Bob Room 9:05 – 10:00am Eugene Demler, Harvard University TBA Bob Room 10:00 – 10:30am Coffee Break Bistro – 1st Floor 10:30 – 11:25am Marcos Rigol, Pennsylvania State University Quantum Quenches in Thermodynamic Limit Bob Room 11:25 – 12:20pm Jens Eisert, Freie University Berlin Dynamical analogue quantum simulators Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:30pm Informal Discussions Bob Room 3:30 – 4:00pm Coffee Break Bob Room 4:00 – 5:00pm Discussion: Experiments Bob Room

Tuesday, May 13th, 2014

 Time Event Location 9:00 – 10:00am Anatoli Polkovnikov TBA Bob Room 10:00 – 10:30am Coffee Break Bistro – 1st Floor 10:30 – 11:25am Fabian Essler, University of Oxford Light-Cone Effects after Quantum Quenches and Excitations at Finite Entropy Bob Room 11:25 – 12:20pm Luca DAlessio Long-time behavior of periodically driven isolated interacting quantum systems Bob Room 12:20 – 12:30pm Conference Photo Atrium 12:30 – 2:00pm Lunch Break Bistro – 2nd Floor 2:00 – 3:30pm Condensed Matter Seminar Federico Becca, SISSA TBA Informal Discussion – Quantum Many Body Dynamics Bob Room   Alice Room 3:30 – 4:00pm Coffee Breaks Bistro – 1st Floor 4:00 – 5:00pm Discussion – Driven Systems Bob Room

Wednesday, May 14, 2014

 Time Event Location 9:00 – 10:00am Ehud Altman Localization and topology protected quantum coherence at the edge of 'hot' matter Bob Room 10:00 – 10:30am Coffee Break Bistro – 1st floor 10:30 – 11:25am Arijeet Pal, Harvard University TBA Bob Room 11:25 – 12:30pm John Imbrie, University of Virginia A Rigorous Result on Many-Body Localization Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:30pm Colloquium Claudia de Rham What can we learn from modifying gravity Theatre 3:30 – 4:00pm Break Bistro – 1st Floor 4:00 – 5:00pm Discussion – Many-Body Localization Bob Room 5:00 Onwards Banquet Bistro – 2nd Floor

Thursday, May 15th, 2014

 Time Event Location 9:00 – 10:00am Jean-Sebastien Caux, University of Amsterdam Exact solutions for quenches in 1d Bose gases and quantum spin chains. Bob Room 10:00 – 10:30am Coffee Break Bistro – 1st Floor 10:30 – 11:25am Ronen Vosk, Weizmann Institute of Science Renormalization group theory of dynamics in many-body localized states and the many-body localization transition Bob Room 11:25 – 12:30pm Matthew Fisher, UC Santa Barbara Can Eigenstate Thermalization Breakdownwithout Disorder? Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:30pm Antonello Scardicchio, Princeton University TBA Bob Room 3:30 – 4:00pm Coffee Break Bistro – 1st Floor 4:00 – 5:00pm Discussion – Localization Without Disorder Bob Room 5:00 Onwards Pub Night Bistro – 1st Floor

Friday, May 16th, 2014

 Time Event Location 9:00 – 10:00am Robert Konik, Brookhaven National Laboratory Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases Bob Room 10:00 – 10:30am Coffee Break Bistro – 1st floor 10:30 – 11:25am Aditi Mitra, New York University Quench dynamics in interacting and disordered field theories in one-dimension Bob Room 11:25 – 12:20pm Lea Santos, Yeshiva University General Features of the Relaxation Dynamics of Isolated Interacting Quantum Systems Bob Room 12:20 – 12:30pm Concluding Remarks Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:30pm Informal Discussions Bob Room 3:30 – 4:00pm Coffee Break Bistro – 1st Floor 4:00 – 6:00pm Informal Discussions Bob Room

Luca DAlessio, Boston University

Long-time behavior of periodically driven isolated interacting quantum systems

We show that generic interacting quantum systems, which are isolated and finite, periodically driven by sudden quenches exhibit three physical regimes. For short driving periods the Floquet Hamiltonian is well approximated by the time-averaged Hamiltonian, while for long periods the evolution operator exhibits properties of random matrices of a Circular Ensemble (CE). In-between, there is a crossover
regime. We argue that, in the thermodynamic limit and for nonvanishing driving periods, the evolution operator always exhibits properties of CE random matrices. Consequently, driving leads to infinite temperature at infinite time and to an unphysical Floquet Hamiltonian.

Ehud Altman, Weizmann Institute of Science

Localization and topology protected quantum coherence at the edge of 'hot' matter

Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently however, it has been established that disorder can localize an isolated many body system, potentially allowing for a sharply defined topological phase even in a highly excited state.I will show this to be the case for the topological phase of a one dimensional magnet with quenched disorder, which features spin one-half excitations at the edges. The time evolution of a simple, highly excited, initial state is used to reveal quantum coherent edge spins. In particular, I will demonstrate, using theoretical arguments and numerical simulation, the coherent revival of an edge spin over a time scale that grows exponentially bigger with system size. This is in sharp contrast to the general expectation that quantum bits strongly coupled to a 'hot' many body system will rapidly lose coherence.

Federico Becca, SISSA

Gapless spin liquids in frustrated Heisenberg models

We present our recent numerical calculations for the Heisenberg model on the square and Kagome lattices, showing that gapless spin liquids may be stabilized in highly-frustrated regimes. In particular, we start from Gutzwiller-projected fermionic states that may describe magnetically disordered phases,[1] and apply few Lanczos steps in order to improve their accuracy. Thanks to the variance extrapolation technique,[2] accurate estimations of the energies are possible, for both the ground state and few low-energy excitations. Our approach suggests that magnetically disordered phases can be described by Abrikosov fermions coupled to gauge fields.

For the Kagome lattice, we find that a gapless U(1) spin liquid with Dirac cones
is competitive with previously proposed gapped spin liquids when only the nearest-neighbor antiferromagnetic interaction is present.[3,4] The inclusion of a next-nearest-neighbor term lead to a Z_2 gapped spin liquid,[5] in agreement with density-matrix renormalization group calculations.[6] In the Heisenberg model on the square lattice with both nearest- and next-nearest-neighbor interactions, a Z_2 spin liquid with gapless spinon excitations is stabilized in the frustrated regime.[7] This results are (partially) in agreement with recent density-matrix renormalization group on large cylinders.[8]

[1] X.-G. Wen, Phys. Rev. B {\bf 44}, 2664 (1991); Phys. Rev. B {\bf 65}, 165113 (2002).
[2] S. Sorella, Phys. Rev. B {\bf 64}, 024512 (2001).
[3] Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405(R) (2013).
[4] Y. Iqbal, D. Poilblanc, and F. Becca, Phys. Rev. B 89, 020407(R) (2014).
[5] W.-J. Hu, Y. Iqbal, F. Becca, D. Poilblanc, and D. Sheng, unpublished.
[6] H.-C. Jiang, Z. Wang, and L. Balents, Nat. Phys. 8, 902 (2012);
S. Yan, D. Huse, and S. White, Science 332, 1173 (2011).
[7] W.-J. Hu, F. Becca, A. Parola, and S. Sorella, Phys. Rev. B 88, 060402(R) (2013).
[8] S.-S. Gong, W.Z., D.N. Sheng, O.I. Motrunich, and M.P.A. Fisher, arXiv:1311.5962 (2013).

Jean-Sebastien Caux, University of Amsterdam

Exact solutions for quenches in 1d Bose gases and quantum spin chains

TBA

Jens Eisert, Freie University Berlin

Dynamical analogue quantum simulators

Complex quantum systems out of equilibrium are at the basis of a number of long-standing questions in physics. This talk will be concerned on the one hand with recent progress on understanding how quantum many-body systems out of equilibrium eventually come to rest, thermalise and cross phase transitions, on the other hand with dynamical analogue quantum simulations using cold atoms [1-4]. In an outlook, we will discuss the question of certification of quantum simulators, and will how this problem also arises in other related settings, such as in Boson samplers [5,6].

[1] S. Braun, M. Friesdorf, S. S. Hodgman, M. Schreiber, J. P. Ronzheimer, A. Riera, M. del Rey, I. Bloch, J. Eisert, U. Schneider, arXiv:1403.7199.
[2] M. Kliesch, M. Kastoryano, C. Gogolin, A. Riera, J. Eisert, arXiv:1309:0816.
[3] S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollwoeck, J. Eisert, I. Bloch, Nature Physics 8, 325 (2012).
[4] A. Riera, C. Gogolin, M. Kliesch, J. Eisert,  in preparation (2014).
[5] C. Gogolin, M. Kliesch, L. Aolita, J. Eisert, in preparation (2014) and arXiv:1306.3995.
[6] S. Aaronson, A. Arkhipov, arXiv:1309.7460.

Fabian Essler, University of Oxford

Light-Cone Effects after Quantum Quenches and Excitations at Finite Entropy

Matthew Fisher, University of California, Santa Barbara

Can Eigenstate Thermalization Breakdown without Disorder?

We describe a new diagnostic for many-body wavefunctions which generalizes the spatial bipartite entanglement entropy. By was of illustration, for a two-component wavefunction of heavy and light particles, a partial (projective) measurement of the coordinates of the heavy (but not light) particles is first performed, and then the entanglement entropy of the projected wavefunction for the light particles is computed. If the two-component wavefunction has a volume law entanglement entropy, yet the post measurement wavefunction of the light particles is disentangled with an area law entanglement, we refer to the original wavefunction as a “Quantum Disentangled State”. This diagnostic can be generalized to include other partial measurements, such as measuring the charge, but not spin, for finite-energy density eigenstates of Fermion Hubbard-type model. Quantum disentanglement results if the post measurement spin-wavefunction has an area law entanglement entropy. Recent numerics searching for such Quantum Disentangled States in 1d Hubbard-type models will be discussed in detail.

John Imbrie, Johns Hopkins University

A Rigorous Result on Many-Body Localization

I will discuss a proof of many-body localization for a one-dimensional spin chain with random local interactions. The proof depends on a physically reasonable assumption that limits the amount of level attraction in the system. I construct a sequence of local rotations that completely diagonalizes the Hamiltonian and exhibits the local degrees of freedom.

Robert Konik, Brookhaven National Laboratory

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

We consider quantum quenches in one dimensional Bose gases where we prepare the gas in the ground state of a parabolic trap and then release it into a small cosine potential.  This cosine potential breaks the integrability of the 1D gas which absent the potential is described by the Lieb-Liniger model.  We explore the consequences of this cosine potential on the thermalization of the gas.  We argue that the integrability breaking of the cosine does not immediately lead to ergodicity inasmuch as we demonstrate that there are residual quasi-conserved quantities post-quench.  We demonstrate that the quality of this quasi-conservation can be made arbitrarily good.

Aditi Mitra, New York University

Quench dynamics in interacting and disordered field theories in one-dimension

I will present results for the quench dynamics of one-dimensional interacting bosons under two circumstances. One is when the bosons are in the vicinity of the superfluid-Mott quantum critical point, while the second is when the bosons are in a disordered potential which can drive the system into a Bose glass phase. I will show that the dynamics following a quench can be quite complex by being characterized by three regimes. One is a short time perturbatively accessible regime which depends on microscopic parameters, the second is an intermediate time prethermalized regime where inelastic effects are weak and correlation functions can show universal scaling behavior which is quantified by a nonequilibrium generalization of the Callan-Symanzik equations. The third is a long time regime where inelastic effects become important. For the dynamics in the inelastic regime I will construct a novel quantum kinetic equation that accounts for multi-particle scattering between bosons, and discuss how the combined effect of interactions and (weak) disorder can thermalize the system.

Arijeet Pal, Harvard University

Many-body mobility edge in a mean-field quantum spin-glass.

Isolated, interacting quantum systems in the presence of strong disorder can exist in a many-body localized phase where the assumptions of equilibrium statistical physics are violated. On tuning either the parameters of the Hamiltonian or the energy density, the system is expected to transition into the ergodic phase. While the transition at "infinite temperature" as a function of system parameters has been found numerically but, the transition tuned by energy density has eluded such methods.
In my talk I will discuss the nature of the many-body localization-delocalization (MBLD) transition as a function of energy denisty in the quantum random energy model (QREM). QREM provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body mobility edge when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition. I will also comment on the nature of the critical states in this mean-field model.
This opens the possibility of developing a mean-field theory of this interesting dynamical phase transition.

Marcos Rigol, Pennsylvania State University

Quantum Quenches in the Thermodynamic Limit

Studies of the quantum dynamics of isolated systems are currently providing fundamental insights into how statistical mechanics emerges under unitary time evolution. Thermalization seems ubiquitous, but experiments with ultracold gases have shown that it need not always occur, particularly near an integrable point. Unfortunately, computational studies of generic (nonintegrable) models are limited to small systems, for which arbitrarily long times can be calculated, or short times, for which large or infinite system sizes can be solved. Consequently, what happens in the thermodynamic limit after long times has been inaccessible to theoretical studies. In this talk, we introduce a linked-cluster based computational approach that allows one to address the latter question in lattice systems. We provide numerical evidence that, in the thermodynamic limit, thermalization occurs in the nonintegrable regime but fails at integrability. A phase transition-like behavior separates the two regimes.

Lea Santos, Yeshiva University

General Features of the Relaxation Dynamics of Isolated Interacting Quantum Systems

We consider isolated interacting quantum systems that are taken out of equilibrium instantaneously (quenched). We study numerically and analytically the probability of finding the initial state later on in time (the so-called fidelity or Loschmidt echo), the relaxation time of the system, and the evolution of few-body observables.  The fidelity decays fastest for systems described by full random matrices, where simultaneous many-body interactions are implied. In the realm of realistic systems with two-body interactions, the dynamics is slower and dependent on the energy of the initial state. The fastest fidelity decay in this case is Gaussian and can persist until saturation. The fidelity also plays a central role in the short-time dynamics of few-body observables that commute with the system Hamiltonian before the quench. Our analyses are mainly developed for initial states that can be prepared in experiments with cold atoms in optical lattices.

Ronen Vosk, Weizmann Institute of Science

Renormalization group theory of dynamics in many-body localized states and the many-body localization transition

It has been argued recently that, through a phenomenon of many-body localization, closed quantum systems subject to sufficiently strong disorder would fail to thermalize. In this talk I will describe a real time renormalization group approach, which offers a controlled description of universal dynamics in the localized phase. In particular it explains the ultra-slow entanglement propagation in this state and identifies the emergent conserved quantities which prevent thermalization. The RG analysis also shows, that far from being a trivial dead state, the MBL state admits phase transitions between distinct dynamical phases. For example, I will discuss the universal aspects of a transition between a paramagnetic localized state to one which exhibits spin-glass order. Finally, I will present a development of the RG scheme, defined on an effective coarse grained model, which allows to capture the transition from a many-body localized to a thermalizing state.

## (Lea Santos) General Features of the Relaxation Dynamics of Isolated Interacting Quantum Systems

Friday May 16, 2014

We consider isolated interacting quantum systems that are taken out of equilibrium instantaneously (quenched). We study numerically and analytically the probability of finding the initial state later on in time (the so-called fidelity or Loschmidt echo), the relaxation time of the system, and the evolution of few-body observables. The fidelity decays fastest for systems described by full random matrices, where simultaneous many-body interactions are implied.

Collection/Series:

## Quench dynamics in interacting and disordered field theories in one-dimension

Friday May 16, 2014
Speaker(s):

I will present results for the quench dynamics of one-dimensional interacting bosons under two circumstances. One is when the bosons are in the vicinity of the superfluid-Mott quantum critical point, while the second is when the bosons are in a disordered potential which can drive the system into a Bose glass phase. I will show that the dynamics following a quench can be quite complex by being characterized by three regimes.

Collection/Series:

## (Robert Konik) Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

Friday May 16, 2014

We consider quantum quenches in one dimensional Bose gases where we prepare the gas in the ground state of a parabolic trap and then release it into a small cosine potential. This cosine potential breaks the integrability of the 1D gas which absent the potential is described by the Lieb-Liniger model. We explore the consequences of this cosine potential on the thermalization of the gas.

Collection/Series:

## TBA

Thursday May 15, 2014
Collection/Series:

## Can Eigenstate Thermalization Breakdown without Disorder?

Thursday May 15, 2014
Speaker(s):

We describe a new diagnostic for many-body wavefunctions which generalizes the spatial bipartite entanglement entropy. By was of illustration, for a two-component wavefunction of heavy and light particles, a partial (projective) measurement of the coordinates of the heavy (but not light) particles is first performed, and then the entanglement entropy of the projected wavefunction for the light particles is computed.

Collection/Series:

## Universal dynamics and topological order in many-body localized states

Thursday May 15, 2014
Speaker(s):

It has been argued recently that, through a phenomenon of many-body localization, closed quantum systems subject to sufficiently strong disorder would fail to thermalize. In this talk I will describe a real time renormalization group approach, which offers a controlled description of universal dynamics in the localized phase. In particular it explains the ultra-slow entanglement propagation in this state and identifies the emergent conserved quantities which prevent thermalization.

Collection/Series:

## (Jean-Sebastien Caux) Exact solutions for quenches in 1d Bose gases and quantum spin chains

Thursday May 15, 2014
Collection/Series:

## A Rigorous Result on Many-Body Localization

Wednesday May 14, 2014
Speaker(s):

I will discuss a proof of many-body localization for a one-dimensional spin chain with random local interactions. The proof depends on a physically reasonable assumption that limits the amount of level attraction in the system. I construct a sequence of local rotations that completely diagonalizes the Hamiltonian and exhibits the local degrees of freedom.

Collection/Series:

## Many-body mobility edge in a mean-field quantum spin-glass

Wednesday May 14, 2014
Speaker(s):

Isolated, interacting quantum systems in the presence of strong disorder can exist in a many-body localized phase where the assumptions of equilibrium statistical physics are violated. On tuning either the parameters of the Hamiltonian or the energy density, the system is expected to transition into the ergodic phase. While the transition at "infinite temperature" as a function of system parameters has been found numerically but, the transition tuned by energy density has eluded such methods.

Collection/Series:

## Localization and topology protected quantum coherence at the edge of 'hot' matter

Wednesday May 14, 2014
Speaker(s):

Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations.

Collection/Series:

## Pages

Scientific Organizers:

Dmitry Abanin, Perimeter Institute
Anushya Chandran, Perimeter Institute
Zlatko Papic, Perimeter Institute