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Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics

Dmitry Abanin University of Geneva (UNIGE) - Department of Theoretical Physics

February 12, 2014 PIRSA:14020127
13/14 PSI - String Theory Review - Lecture 12

Davide Gaiotto Perimeter Institute for Theoretical Physics

February 12, 2014 PIRSA:14020032
Geometrical dependence of information in 2d critical systems

Paul Fendley University of Oxford

February 12, 2014 PIRSA:14020119
13/14 PSI - Cosmology Review - Lecture 11

Latham Boyle Perimeter Institute for Theoretical Physics

February 12, 2014 PIRSA:14020021
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators.

Max Metlitski Massachusetts Institute of Technology (MIT) - Department of Physics

February 12, 2014 PIRSA:14020120
Quantum Tapestries

Matthew Fisher Kavli Institute for Theoretical Physics (KITP)

February 12, 2014 PIRSA:14020121
Applications of Information Theory in Direct Sum and Direct Product Problems
February 12, 2014 PIRSA:14020142
Quantum Information
13/14 PSI - Condensed Matter Review - Lecture 13

Alioscia Hamma Università degli Studi di Napoli Federico II

February 13, 2014 PIRSA:14020106
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
- Guifre Vidal Google
- Lukasz Cincio Los Alamos National Laboratory
February 13, 2014 PIRSA:14020122
Interacting electronic topological insulators in three dimensions

Senthil Todadri Massachusetts Institute of Technology (MIT) - Department of Physics

February 13, 2014 PIRSA:14020123
13/14 PSI - String Theory Review - Lecture 13

Davide Gaiotto Perimeter Institute for Theoretical Physics

February 13, 2014 PIRSA:14020033
Incoherent metals

Brian Swingle University of Maryland - College Park

February 13, 2014 PIRSA:14020124

Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics

Dmitry Abanin University of Geneva (UNIGE) - Department of Theoretical Physics

February 12, 2014 PIRSA:14020127

We demonstrate that the many-body localized phase is characterized by the existence of infinitely many local conservation laws. We argue that many-body eigenstates can be obtained from product states by a sequence of nearly local unitary transformation, and therefore have an area-law entanglement entropy, typical of ground states. Using this property, we construct the local integrals of motion in terms of projectors onto certain linear combinations of eigenstates [1]. The local integrals of motion can be viewed as effective quantum bits which have a conserved z-component that cannot decay. Thus, the dynamics is reduced to slow dephasing between distant effective bits. For initial product states, this leads to a characteristic slow power-law decay of local observables, which is measurable experimentally, as well as to logarithmic in time growth of entanglement entropy [2,3]. We support our findings by numerical simulations of random-field XXZ spin chains. Our work shows that the many-body localized phase is locally integrable, reveals a simple entanglement structure of eigenstates, and establishes the laws of dynamics in this phase.

[1] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. Lett. 111, 127201 (2013).
[2] Jens H. Bardarson, Frank Pollmann, and Joel E. Moore, Phys. Rev. Lett. 109, 017202 (2012).
[3] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. Lett. 110, 260601 (2013)
13/14 PSI - String Theory Review - Lecture 12

Davide Gaiotto Perimeter Institute for Theoretical Physics

February 12, 2014 PIRSA:14020032
Geometrical dependence of information in 2d critical systems

Paul Fendley University of Oxford

February 12, 2014 PIRSA:14020119

In both classical and quantum critical systems, universal contributions to the mutual information and Renyi entropy depend on geometry. I will first explain how in 2d classical critical systems on a rectangle, the mutual information depends on the central charge in a fashion making its numerical extraction easy, as in 1d quantum systems. I then describe analogous results for 2d quantum critical systems. Specifically, in special 2d quantum systems such as quantum dimer/Lifshitz models, the leading geometry-dependent term in the Renyi entropies can be computed exactly. In more common 2d quantum systems, numerical computations of a corner term hint toward the existence of a universal quantity providing a measure of the number of degrees of freedom analogous to the central charge.
13/14 PSI - Cosmology Review - Lecture 11

Latham Boyle Perimeter Institute for Theoretical Physics

February 12, 2014 PIRSA:14020021
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators.

Max Metlitski Massachusetts Institute of Technology (MIT) - Department of Physics

February 12, 2014 PIRSA:14020120

A 3d electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface termination of an ETI supports an odd number of Dirac cones. In this talk, I will show that in the presence of strong interactions, an ETI surface can actually be gapped and symmetry preserving, at the cost of carrying an intrinsic two-dimensional topological order. I will argue that such a topologically ordered phase can be obtained from the surface superconductor by proliferating the flux 2hc/e vortex. The resulting topological order consists of two sectors: a Moore-Read sector, which supports non-Abelian charge e/4 anyons, and an Abelian anti-semion sector, which is electrically neutral. The time-reversal and particle number symmetries are realized in this surface phase in an "anomalous" way: one which is impossible in a strictly 2d system. If time permits, I will discuss related results on topologically ordered surface phases of 3d topological superconductors.
Quantum Tapestries

Matthew Fisher Kavli Institute for Theoretical Physics (KITP)

February 12, 2014 PIRSA:14020121

Within each of nature's crystals is an exotic quantum world of electrons weaving to and fro. Each crystal has it's own unique tapestry, as varied as the crystals themselves. In some crystals, the electrons weave an orderly quilt. Within others, the electrons are seemingly entwined in an entangled web of quantum motion. In this talk, I will describe the ongoing efforts to disentangle even nature's most intricate quantum embroidery. Cutting-edge quantum many-body simulations together with recent ideas from quantum information theory, such as entanglement entropy, are enabling a coherent picture to emerge.
Applications of Information Theory in Direct Sum and Direct Product Problems
February 12, 2014 PIRSA:14020142
Quantum Information
A fundamental question in complexity theory is how much resource is needed to solve k independent instances of a problem compared to the resource required to solve one instance. Suppose solving one instance of a problem with probability of correctness p, we require c units of some resource in a given model of computation. A direct sum theorem states that in order to compute k independent instances of a problem, it requires k times units of the resource needed to compute one instance. A strong direct product theorem states that, with o(k • c) units of the resource, one can only compute all the k instances correctly with probability exponentially small in k. In this talk, I am going to present some of recent progress on direct sum and direct product theorems in the model of communication complexity and two-prover one-round games with information-theoretic approach. The talk is based on parts of my doctoral work.
13/14 PSI - Condensed Matter Review - Lecture 13

Alioscia Hamma Università degli Studi di Napoli Federico II

February 13, 2014 PIRSA:14020106
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
- Guifre Vidal Google
- Lukasz Cincio Los Alamos National Laboratory
February 13, 2014 PIRSA:14020122

Topological phases in frustrated quantum spin systems have fascinated researchers for decades. One of the earliest proposals for such a phase was the chiral spin liquid put forward by Kalmeyer and Laughlin in 1987 as the bosonic analogue of the fractional quantum Hall effect. Elusive for many years, recent times have finally seen a number of models that realize this phase. However, these models are somewhat artificial and unlikely to be found in realistic materials.
Here, we take an important step towards the goal of finding a chiral spin liquid in nature by examining a physically motivated model for a Mott insulator on the Kagome lattice with broken time-reversal symmetry. We first provide a theoretical justification for the emergent chiral spin liquid phase in terms of a network model perspective. We then present an unambiguous numerical identification and characterization of the universal topological properties of the phase, including ground state degeneracy, edge physics, and anyonic bulk excitations, by using a variety of powerful numerical probes, including the entanglement spectrum and modular transformations.
Interacting electronic topological insulators in three dimensions

Senthil Todadri Massachusetts Institute of Technology (MIT) - Department of Physics

February 13, 2014 PIRSA:14020123

I will review recent progress in describing interacting electronic topological insulators/superconductors in three dimensions. The focus will be on Symmetry Protected Topological (SPT) phases of electronic systems with charge conservation and time reversal. I will argue that the well known Z2 classification of free fermion insulators with this important symmetry generalizes to a Z2^3 classification in the presence of interactions. I will describe the experimental fingerprints and other physical properties of these states. If time permits, I will describe results on the classification and properties of 3d electronic SPT states with various other physically relevant symmetries.
13/14 PSI - String Theory Review - Lecture 13

Davide Gaiotto Perimeter Institute for Theoretical Physics

February 13, 2014 PIRSA:14020033
Incoherent metals

Brian Swingle University of Maryland - College Park

February 13, 2014 PIRSA:14020124

I'll talk about some work in progress concerning the topic of metals which have no coherent quasiparticles. In particular, I'll compare and contrast the ubiquitous near horizon AdS2 region appearing in holographic models with a phase of matter called the spin incoherent luttinger liquid. By analyzing the structure of entanglement and correlations, we will find many similarities between these two states of matter. An interpretation of some incoherent metals as describing intermediate scale renormalization group fixed poins with an infinite number of relevant directions will also be discussed.

Title	Speaker(s)	Date	Collection	Type	Info	Relevance
Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics	Dmitry Abanin	2014‑02‑12	Emergence in Complex Systems	Conference	View details	1
13/14 PSI - String Theory Review - Lecture 12	Davide Gaiotto	2014‑02‑12	13/14 PSI - String Theory Review	Course	View details	1
Geometrical dependence of information in 2d critical systems	Paul Fendley	2014‑02‑12	Emergence in Complex Systems	Conference	View details	1
13/14 PSI - Cosmology Review - Lecture 11	Latham Boyle	2014‑02‑12	13/14 PSI - Cosmology Review	Course	View details	1
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators.	Max Metlitski	2014‑02‑12	Emergence in Complex Systems	Conference	View details	1
Quantum Tapestries	Matthew Fisher	2014‑02‑12	Emergence in Complex Systems	Conference	View details	1
Applications of Information Theory in Direct Sum and Direct Product Problems		2014‑02‑12	Perimeter Institute Quantum Discussions	Scientific Series	View details	1
13/14 PSI - Condensed Matter Review - Lecture 13	Alioscia Hamma	2014‑02‑13	13/14 PSI - Condensed Matter Review	Course	View details	1
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator	Guifre Vidal, Lukasz Cincio	2014‑02‑13	Emergence in Complex Systems	Conference	View details	1
Interacting electronic topological insulators in three dimensions	Senthil Todadri	2014‑02‑13	Emergence in Complex Systems	Conference	View details	1
13/14 PSI - String Theory Review - Lecture 13	Davide Gaiotto	2014‑02‑13	13/14 PSI - String Theory Review	Course	View details	1
Incoherent metals	Brian Swingle	2014‑02‑13	Emergence in Complex Systems	Conference	View details	1

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