Quantum Many-Body Dynamics

18 talks

May 12, 2014 - May 16, 2014

C14024

Collection Type

Conference/School

Description

Quantum Many-Body Dynamics

Displaying 1 - 12 of 18

TBA

Eugene Demler
Harvard University

May 12, 2014

PIRSA:14050065
Quantum Quenches in Thermodynamic Limit

Marcos Rigol
Pennsylvania State University

May 12, 2014

PIRSA:14050067
Dynamical analogue quantum simulators

Jens Eisert
Freie Universität Berlin

May 12, 2014

PIRSA:14050068
Anatoli Polkovnikov - Deriving effective Floquet Hamiltonians in interacting systems using the Magnus expansion

May 13, 2014

PIRSA:14050071
Light-Cone Effects after Quantum Quenches and Excitations at Finite Entropy

Fabian Essler
University of Oxford

May 13, 2014

PIRSA:14050072
Long-time behavior of periodically driven isolated interacting quantum systems

Luca D'Alessio
Boston University

May 13, 2014

PIRSA:14050073
Gapless spin liquids in frustrated Heisenberg models

Federico Becca
SISSA International School for Advanced Studies
May 13, 2014

PIRSA:14050074
Condensed Matter
Localization and topology protected quantum coherence at the edge of 'hot' matter

Ehud Altman
University of California, Berkeley

May 14, 2014

PIRSA:14050077
Many-body mobility edge in a mean-field quantum spin-glass

Arijeet Pal
Harvard University

May 14, 2014

PIRSA:14050078
A Rigorous Result on Many-Body Localization

John Imbrie
University of Virginia

May 14, 2014

PIRSA:14050079
What can we learn from modifing gravity ?

Claudia de Rham
Imperial College London
May 14, 2014

PIRSA:14050003
Cosmology
(Jean-Sebastien Caux) Exact solutions for quenches in 1d Bose gases and quantum spin chains

May 15, 2014

PIRSA:14050081

TBA

Eugene Demler
Harvard University

May 12, 2014

PIRSA:14050065
Quantum Quenches in Thermodynamic Limit

Marcos Rigol
Pennsylvania State University

May 12, 2014

PIRSA:14050067

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.
Dynamical analogue quantum simulators

Jens Eisert
Freie Universität Berlin

May 12, 2014

PIRSA:14050068

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.
Anatoli Polkovnikov - Deriving effective Floquet Hamiltonians in interacting systems using the Magnus expansion

May 13, 2014

PIRSA:14050071
Light-Cone Effects after Quantum Quenches and Excitations at Finite Entropy

Fabian Essler
University of Oxford

May 13, 2014

PIRSA:14050072
Long-time behavior of periodically driven isolated interacting quantum systems

Luca D'Alessio
Boston University

May 13, 2014

PIRSA:14050073

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.
Gapless spin liquids in frustrated Heisenberg models

Federico Becca
SISSA International School for Advanced Studies
May 13, 2014

PIRSA:14050074
Condensed Matter
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).
Localization and topology protected quantum coherence at the edge of 'hot' matter

Ehud Altman
University of California, Berkeley

May 14, 2014

PIRSA:14050077

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

Arijeet Pal
Harvard University

May 14, 2014

PIRSA:14050078

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.
A Rigorous Result on Many-Body Localization

John Imbrie
University of Virginia

May 14, 2014

PIRSA:14050079

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.
What can we learn from modifing gravity ?

Claudia de Rham
Imperial College London
May 14, 2014

PIRSA:14050003
Cosmology
I will review models of modified gravity in the infrared and show how extra degrees of freedom present in these theories get screened via the Vainshtein mechanism. That mechanism comes hand in hand with its own share of peculiarities: classical superluminalities, strong coupling and perturbative non-analyticity of the S-matrix to name a few. From a traditional effective field viewpoint such effects are disastrous but I will present the first hints in understanding these theories beyond the traditional perspective and their implications not only for gravity but also for our understanding of a certain class of field theories.
(Jean-Sebastien Caux) Exact solutions for quenches in 1d Bose gases and quantum spin chains

May 15, 2014

PIRSA:14050081

Title	Speaker(s)	Date	Talk Type	Info
TBA	Eugene Demler	2014-05-12	Conference	View details
Quantum Quenches in Thermodynamic Limit	Marcos Rigol	2014-05-12	Conference	View details
Dynamical analogue quantum simulators	Jens Eisert	2014-05-12	Conference	View details
Anatoli Polkovnikov - Deriving effective Floquet Hamiltonians in interacting systems using the Magnus expansion		2014-05-13	Conference	View details
Light-Cone Effects after Quantum Quenches and Excitations at Finite Entropy	Fabian Essler	2014-05-13	Conference	View details
Long-time behavior of periodically driven isolated interacting quantum systems	Luca D'Alessio	2014-05-13	Conference	View details
Gapless spin liquids in frustrated Heisenberg models	Federico Becca	2014-05-13	Scientific Series	View details
Localization and topology protected quantum coherence at the edge of 'hot' matter	Ehud Altman	2014-05-14	Conference	View details
Many-body mobility edge in a mean-field quantum spin-glass	Arijeet Pal	2014-05-14	Conference	View details
A Rigorous Result on Many-Body Localization	John Imbrie	2014-05-14	Conference	View details
What can we learn from modifing gravity ?	Claudia de Rham	2014-05-14	Scientific Series	View details
(Jean-Sebastien Caux) Exact solutions for quenches in 1d Bose gases and quantum spin chains		2014-05-15	Conference	View details

Quantum Many-Body Dynamics

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