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Entanglement, Ergodicity, and Many-Body Localization

Dmitry Abanin Princeton University

May 01, 2014

PIRSA:14050020
Localization-Protected Quantum Order

David Huse Princeton University

May 01, 2014

PIRSA:14050013
Welcome Address

Michel Gingras University of Waterloo

May 01, 2014

PIRSA:14050012
Quantum thermalization and many-body Anderson localization

David Huse Princeton University
April 30, 2014

PIRSA:14040066
Quantum Physics
Probing renormalization group flows using entanglement entropy

Mark Mezei Massachusetts Institute of Technology (MIT)
April 30, 2014

PIRSA:14040144
High Energy Physics
Helical edge resistance introduced by charge disorder

Leonid Glazman Yale University
April 29, 2014

PIRSA:14040082
Condensed Matter
Localizing Braneworlds in Infinite Spaces

Kellogg Stelle Imperial College London
April 29, 2014

PIRSA:14040064
High Energy Physics
Galileon Maps: Inequivalent Coset Constructions for Spacetime Symmetries

Gabirele Trevisan SISSA International School for Advanced Studies
April 29, 2014

PIRSA:14040132
Astrophysics
3d N = 4 Gauge Theories, Mirror Symmetry and Hilbert series

Noppadol Mekareeya Imperial College London
April 28, 2014

PIRSA:14040143
High Energy Physics
Double scaling in tensor models

James Ryan Vinted (Germany)

April 25, 2014

PIRSA:14040114
Between Matrices and Tensors

Vincent Rivasseau University of Paris-Saclay

April 25, 2014

PIRSA:14040113
Renormalization group approach to 3d group field theory

Sylvain Carrozza University of Burgundy

April 25, 2014

PIRSA:14040112

Entanglement, Ergodicity, and Many-Body Localization

Dmitry Abanin Princeton University

May 01, 2014

PIRSA:14050020

We are used to describing systems of many particles by statistical mechanics. However, the basic postulate of statistical mechanics – ergodicity – breaks down in so-called many-body localized systems, where disorder prevents particle transport and thermalization. In this talk, I will present a theory of the many-body localized (MBL) phase, based on new insights from quantum entanglement. I will argue that, in contrast to ergodic systems, MBL eigenstates are not highly entangled. I will use this fact to show that MBL phase is characterized by an infinite number of emergent local conservation laws, in terms of which the Hamiltonian acquires a universal form. Turning to the experimental implications, I will describe the response of MBL systems to quenches: surprisingly, entanglement shows logarithmic in time growth, reminiscent of glasses, while local observables exhibit power-law approach to “equilibrium” values. I will support the presented theory with results of numerical experiments. I will close by discussing other directions in exploring ergodicity and its breaking in quantum many-body systems.
Localization-Protected Quantum Order

David Huse Princeton University

May 01, 2014

PIRSA:14050013

Systems that are many-body Anderson localized can exhibit symmetry-breaking long-range order or topological order in regimes where such order would be destroyed at equilibrium by thermal fluctuations. The ordering is dynamical: an ordered initial state stays ordered, being "protected" by the localization of all fluctuations. The simplest examples are quantum Ising models with static randomness. For the random quantum Ising chain this feature has been "known" but apparently not appreciated for close to half a century.

Ref.: Huse, et al., Phys. Rev. B 88, 014206 (2013).
Welcome Address

Michel Gingras University of Waterloo

May 01, 2014

PIRSA:14050012
Quantum thermalization and many-body Anderson localization

David Huse Princeton University
April 30, 2014

PIRSA:14040066
Quantum Physics
Progress in physics and quantum information science motivates much recent study of the behavior of strongly-interacting many-body quantum systems fully isolated from their environment, and thus undergoing unitary time evolution. What does it mean for such a system to go to thermal equilibrium? I will explain the Eigenstate Thermalization Hypothesis (ETH), which posits that each individual exact eigenstate of the system's Hamiltonian is at thermal equilibrium, and which appears to be true for most (but not all) quantum many-body systems. Prominent among the systems that do not obey this hypothesis are quantum systems that are many-body Anderson localized and thus do not constitute a reservoir that can thermalize itself. When the ETH is true, one can do standard statistical mechanics using the `single-eigenstate ensembles', which are the limit of the microcanonical ensemble where the `energy window' contains only a single many-body quantum state. These eigenstate ensembles are more powerful than the traditional statistical mechanical ensembles, in that they can also "see" the quantum phase transition in to the localized phase, as well as a rich new world of phases and phase transitions within the localized phase.
Probing renormalization group flows using entanglement entropy

Mark Mezei Massachusetts Institute of Technology (MIT)
April 30, 2014

PIRSA:14040144
High Energy Physics
The entanglement entropy of the vacuum of a quantum field theory contains information about physics at all scales and is UV sensitive. A simple refinement of entanglement entropy gets rid of its UV divergence, and allows us to extract entanglement per scale. In two and three spacetime dimensions this quantity can be used as a proxy for the number of degrees of freedom, as it decreases under RG flow. We investigate its behavior around fixed points, and reveal its interesting analytic structure in the space of couplings.
Helical edge resistance introduced by charge disorder

Leonid Glazman Yale University
April 29, 2014

PIRSA:14040082
Condensed Matter
Electron puddles created by doping of a 2D topological insulator may violate the ideal helical edge conductance. Because of a long electron dwelling time, even a single puddle may lead to a significant inelastic backscattering. We find the resulting correction to the perfect edge conductance. Generalizing to multiple puddles, we assess the dependence of the helical edge resistance on temperature and on the doping level. Puddles with odd electron number carry a spin and lead to a logarithmically-weak temperature dependence of the resistivity of a long edge. The developed theory provides a framework for analyzing the results of the past and ongoing electron transport experiments with 2D topological insulators
Localizing Braneworlds in Infinite Spaces

Kellogg Stelle Imperial College London
April 29, 2014

PIRSA:14040064
High Energy Physics
There have been a number of attempts to achieve a localization of gravity on a braneworld hypersurface embedded in an infinite spacetime, but these have all fallen short of what might be desired, for various reasons. There have even been no-go theorems claimed for constructions made using just accepted elements of string or M theory. The talk will present a proposed resolution of this problem based upon a hyperbolic solution of type IIA theory with a superposed NS-5 brane. Gravity is bound to the brane surface owing to the existence of a single normalizable bound state of the transverse space Laplacian.
Galileon Maps: Inequivalent Coset Constructions for Spacetime Symmetries

Gabirele Trevisan SISSA International School for Advanced Studies
April 29, 2014

PIRSA:14040132
Astrophysics
Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. In this talk I will analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds.
3d N = 4 Gauge Theories, Mirror Symmetry and Hilbert series

Noppadol Mekareeya Imperial College London
April 28, 2014

PIRSA:14040143
High Energy Physics
This talk focuses on vacuum moduli spaces of N=4 supersymmetric field theories in three dimensions. A particular branch of the moduli space, known as the Coulomb branch, receives quantum corrections. We present an exact result, known as the Hilbert series, that enumerates the operators in the chiral ring of such a quantum Coulomb branch. This exact result can be applied to a large class of 3d supersymmetric field theories, with and without known Lagrangian descriptions. As an application, we present a method to compute partition functions of instantons on C^2 for any simple group, including exceptional and non-simply-laced ones.
Double scaling in tensor models

James Ryan Vinted (Germany)

April 25, 2014

PIRSA:14040114

I present recent work on the double scaling limit of random tensor models through the analysis of their Schwinger-Dyson equations. This study exemplifies their potential for probing the continuum phase structure of these theories.
Between Matrices and Tensors

Vincent Rivasseau University of Paris-Saclay

April 25, 2014

PIRSA:14040113

Quartic tensor models can be rewritten in terms of intermediate matrix fields. The corresponding expansion is not only simpler, it suggests also new bridges between matrices, strings and tensors.
Renormalization group approach to 3d group field theory

Sylvain Carrozza University of Burgundy

April 25, 2014

PIRSA:14040112

I will start with a brief overview of tensorial group field theories with gauge invariant condition and their relation to spin foam models. The rest of the talk will be focused on the SU(2) theory in dimension 3, which is related to Euclidean 3d quantum gravity and has been proven renormalizable up to order 6 interactions. General renormalization group flow equations will be introduced, allowing in particular to understand the behavior of the relevant couplings in the neighborhood of the Gaussian fixed point. I will close with preliminary investigations about the existence of a non-trivial fixed point.

Title	Date	Collection	Type	Info
Entanglement, Ergodicity, and Many-Body Localization	2014‑05‑01	4 Corners Southwest Ontario Condensed Matter Physics Symposium 2014	Conference	View details
Localization-Protected Quantum Order	2014‑05‑01	4 Corners Southwest Ontario Condensed Matter Physics Symposium 2014	Conference	View details
Welcome Address	2014‑05‑01	4 Corners Southwest Ontario Condensed Matter Physics Symposium 2014	Conference	View details
Quantum thermalization and many-body Anderson localization	2014‑04‑30	Colloquium	Scientific Series	View details
Probing renormalization group flows using entanglement entropy	2014‑04‑30	Quantum Fields and Strings	Scientific Series	View details
Helical edge resistance introduced by charge disorder	2014‑04‑29	Quantum Matter	Scientific Series	View details
Localizing Braneworlds in Infinite Spaces	2014‑04‑29	Quantum Fields and Strings	Scientific Series	View details
Galileon Maps: Inequivalent Coset Constructions for Spacetime Symmetries	2014‑04‑29	Cosmology and Gravitation	Scientific Series	View details
3d N = 4 Gauge Theories, Mirror Symmetry and Hilbert series	2014‑04‑28	Quantum Fields and Strings	Scientific Series	View details
Double scaling in tensor models	2014‑04‑25	Renormalization Group Approaches to Quantum Gravity	Conference	View details
Between Matrices and Tensors	2014‑04‑25	Renormalization Group Approaches to Quantum Gravity	Conference	View details
Renormalization group approach to 3d group field theory	2014‑04‑25	Renormalization Group Approaches to Quantum Gravity	Conference	View details

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Format results

Entanglement, Ergodicity, and Many-Body Localization

Localization-Protected Quantum Order

Welcome Address

Quantum thermalization and many-body Anderson localization

Probing renormalization group flows using entanglement entropy

Helical edge resistance introduced by charge disorder

Localizing Braneworlds in Infinite Spaces

Galileon Maps: Inequivalent Coset Constructions for Spacetime Symmetries

3d N = 4 Gauge Theories, Mirror Symmetry and Hilbert series

Double scaling in tensor models

Between Matrices and Tensors

Renormalization group approach to 3d group field theory

Entanglement, Ergodicity, and Many-Body Localization

Localization-Protected Quantum Order

Welcome Address

Quantum thermalization and many-body Anderson localization

Probing renormalization group flows using entanglement entropy

Helical edge resistance introduced by charge disorder

Localizing Braneworlds in Infinite Spaces

Galileon Maps: Inequivalent Coset Constructions for Spacetime Symmetries

3d N = 4 Gauge Theories, Mirror Symmetry and Hilbert series

Double scaling in tensor models

Between Matrices and Tensors

Renormalization group approach to 3d group field theory