Conference

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Gauging symmetry of 2D topological phases

Zhenghan Wang Microsoft Corporation

February 13, 2014

PIRSA:14020125
Incoherent metals

Brian Swingle Brandeis University

February 13, 2014

PIRSA:14020124
Interacting electronic topological insulators in three dimensions

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

February 13, 2014

PIRSA:14020123
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
- Guifre Vidal Alphabet (United States)
- Lukasz Cincio Los Alamos National Laboratory
February 13, 2014

PIRSA:14020122
Quantum Tapestries

Matthew Fisher University of California, Santa Barbara

February 12, 2014

PIRSA:14020121
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
Geometrical dependence of information in 2d critical systems

Paul Fendley University of Oxford

February 12, 2014

PIRSA:14020119
Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics

Dmitry Abanin Princeton University

February 12, 2014

PIRSA:14020127
Geometry of topological matter: some examples

Duncan Haldane Princeton University

February 12, 2014

PIRSA:14020117
Fractional Quantum Hall Effect in a curved space

Pavel Wiegmann

February 11, 2014

PIRSA:14020112
Tuning magnetism and Chern bands in spin-orbit coupled double perovskites

Arun Paramekanti University of Toronto

February 11, 2014

PIRSA:14020116
Topological response in gapless systems: from Weyl semimetals to metallic ferromagnets

Anton Burkov University of Waterloo

February 11, 2014

PIRSA:14020115

Gauging symmetry of 2D topological phases

Zhenghan Wang Microsoft Corporation

February 13, 2014

PIRSA:14020125

I will discuss the mathematical framework for gauging a local unitary finite group symmetry of a 2D topological phase of matter.
Incoherent metals

Brian Swingle Brandeis University

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.
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.
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
- Guifre Vidal Alphabet (United States)
- 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.
Quantum Tapestries

Matthew Fisher University of California, Santa Barbara

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

Dmitry Abanin Princeton University

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)
Geometry of topological matter: some examples

Duncan Haldane Princeton University

February 12, 2014

PIRSA:14020117

I will look at two cases of the interplay of geometry (curvature) and topology:
(1) 3D Topological metals: how to understand their surface "Fermi arcs" in terms of their emergent conservation laws and the Streda formula for the non-quantized anomalous Hall effect.
(2) The Hall viscosity tensor in the FQHE as a local field, and its Gaussian-curvature response that allows local compression or expansion of the fluid to accommodate substrate inhomogeneity.
Fractional Quantum Hall Effect in a curved space

Pavel Wiegmann

February 11, 2014

PIRSA:14020112

We developed a general method to compute the correlation functions of FQH states on a curved space. The computation features the gravitational trace anomaly and reveals geometric properties of FQHE. Also we highlight a relation between the gravitational and electromagnetic response functions. The talk is based on the recent paper with T. Can and M. Laskin.
Tuning magnetism and Chern bands in spin-orbit coupled double perovskites

Arun Paramekanti University of Toronto

February 11, 2014

PIRSA:14020116

We show that double perovskites with 3d and 5d transition metal ions exhibit spin-orbit coupled magnetic excitations, finding good agreement with neutron scattering experiments in bulk powder samples. Motivated by experimental developments in the field of oxide heterostructures, we also study double perovskites films grown along the [111] direction. We show that spin-orbit coupling in such low dimensional systems can drive ferromagnetic order due to electronic correlations. This results in topological Chern bands, with symmetry-allowed trigonal deformations leading to quantum anomalous Hall states supporting a pair of chiral edge modes.
Topological response in gapless systems: from Weyl semimetals to metallic ferromagnets

Anton Burkov University of Waterloo

February 11, 2014

PIRSA:14020115

Standard picture of a topologically-nontrivial phase of matter is an insulator with a bulk energy gap, but metallic surface states, protected by the bulk gap. Recent work has shown, however, that certain gapless systems may also be topologically nontrivial, in a precise and experimentally observable way. In this talk I will review our work on a class of such systems, in which the nontrivial topological properties arise from the existence of nondegenerate point band-touching nodes (Weyl nodes) in their electronic structure. Weyl nodes generally exist in any three-dimensional material with a broken time-reversal or inversion symmetry. Their effect is particularly striking, however, when the nodes coincide with the Fermi energy and no other states at the Fermi energy exist. Such "Weyl semimetals" have vanishing bulk density of states, but have gapless metallic surface states with an open (unlike in a regular two-dimensional metal) Fermi surface ("Fermi arc"). I will discuss our proposal to realize Weyl semimetal state in a heterostructure, consisting of alternating layers of topological and ordinary insulator, doped with magnetic impurities. I will further show that, apart from Weyl semimetals, even such "ordinary" materials as common metallic ferromagnets, in fact also possess Weyl nodes in the electronic structure, leading to the appearance of chiral Fermi-arc surface states and the corresponding contribution to their intrinsic anomalous Hall conductivity.

Title	Speaker(s)	Date	Talk Type	Info link
Gauging symmetry of 2D topological phases	Zhenghan Wang	2014-02-13	Conference	View details
Incoherent metals	Brian Swingle	2014-02-13	Conference	View details
Interacting electronic topological insulators in three dimensions	Senthil Todadri	2014-02-13	Conference	View details
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator	Guifre Vidal, Lukasz Cincio	2014-02-13	Conference	View details
Quantum Tapestries	Matthew Fisher	2014-02-12	Conference	View details
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators.	Max Metlitski	2014-02-12	Conference	View details
Geometrical dependence of information in 2d critical systems	Paul Fendley	2014-02-12	Conference	View details
Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics	Dmitry Abanin	2014-02-12	Conference	View details
Geometry of topological matter: some examples	Duncan Haldane	2014-02-12	Conference	View details
Fractional Quantum Hall Effect in a curved space	Pavel Wiegmann	2014-02-11	Conference	View details
Tuning magnetism and Chern bands in spin-orbit coupled double perovskites	Arun Paramekanti	2014-02-11	Conference	View details
Topological response in gapless systems: from Weyl semimetals to metallic ferromagnets	Anton Burkov	2014-02-11	Conference	View details

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