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# Emergence in Complex Systems

Conference Date:
Lundi, Février 10, 2014 (All day) to Vendredi, Février 14, 2014 (All day)
Pirsa Collection:
Scientific Areas:
Condensed Matter

This mini-program will focus on quantum materials, models and field theories where strong correlations result in novel emergent phenomena.  The aim will be to highlight advances in the theory of magnetism, topological phases, superconductivity, entanglement, many-body localization, and other topics of recent interest.

The program will consist of organized talks in the morning, with the afternoons free for collaboration.  Seminar rooms will be available in the afternoon for participants to organize their own informal discussions.

• Dmitry Abanin, Perimeter Institute
• Ganapathy Baskaran, The Institute of Mathematical Sciences Chennai
• Anton Burkov, University of Waterloo
• Anushya Chandran, Perimeter Institute
• Lukasz Cincio, Perimeter Institute
• Paul Fendley, University of Virginia
• Matthew Fisher, University of California, Santa Barbara
• Zheng-Cheng Gu, Perimeter Institute
• Duncan Haldane, Princeton University
• David Hawthorn, University of Waterloo
• Jan Kycia, University of Waterloo
• Chris Laumann, Princeton University
• Yuan-Ming Lu, University of California, Berkeley
• Max Metlitski, University of California, Santa Barbara
• Zlatko Papic, Perimeter Institute
• Arun Paramekanti, University of Toronto
• Luiz Santos, Perimeter Institute
• Brian Swingle, Harvard University
• Senthil Todadri, Massachusetts Institute of Technology
• Guifre Vidal, Perimeter Institute
• Zhenghan Wang, Microsoft Station Q
• Pavel Wiegmann, University of Chicago
• Dmitry Abanin, Perimeter Institute
• Ganapathy Baskaran, The Institute of Mathematical Sciences Chennai
• Hector Bombin, Perimeter Institute
• Jacob Bridgeman, Perimeter Institute
• Oliver Buerschaper, Perimeter Institute
• Anton Burkov, University of Waterloo
• Juan Carrasquillia, Perimeter Institute
• Hilary Carteret, Wilfrid Laurier University
• Anushya Chandran, Perimeter Institute
• Yangang Chen, Perimeter Institute
• Lukasz Cincio, Perimeter Institute
• Alexandre Day, University of Waterloo
• Paul Fendley, University of Virginia
• Matthew Fisher, University of California, Santa Barbara
• Zheng-Cheng Gu, Perimeter Institute
• Duncan Haldane, Princeton University
• David Hawthorn, University of Waterloo
• Lauren Hayward, University of Waterloo
• Huan He, Perimeter Institute
• Ann Kallin, University of Waterloo
• Isaac Kim, Perimeter Institute
• Bohdan Kulchytskyy, University of Waterloo
• Jan Kycia, University of Waterloo
• Tian Lan, Perimeter Institute
• Chris Laumann, Princeton University
• Keith Lee, Perimeter Institute
• Sung-Sik Lee, Perimeter Institute & McMaster University
• Michael Levin, University of Chicago
• Jimmy Fangzhou Liu, Massachusetts Institute of Technology
• Yuan-Ming Lu, University of California, Berkeley
• Peter Lunts, Perimeter Institute
• Ipsita Mandal, Perimeter Institute
• Roger Melko, Perimeter Institute & University of Waterloo
• Max Metlitski, University of California, Santa Barbara
• Rob Myers, Perimeter Institute
• Zlatko Papic, Perimeter Institute
• Arun Paramekanti, University of Toronto
• Subir Sachdev, Harvard University
• Luiz Santos, Perimeter Institute
• Miles Stoudenmire, Perimeter Institute
• Brian Swingle, Harvard University
• Evelyn Tang, Massachusetts Institute of Technology
• Senthil Todadri, Massachusetts Institute of Technology
• Guifre Vidal, Perimeter Institute
• Yidun Wan, Perimeter Institute
• Juven Wang, Massachusetts Institute of Technology
• Zhenghan Wang, Microsoft Station Q
• Xiao-Gang Wen, Perimeter Institute
• Pavel Wiegmann, University of Chicago
• William Witczak-Krempa, Perimeter Institute
• Peng Ye, Perimeter Institute

Monday, February 10, 2014

 Time Event Location 8:30 – 9:00am Registration Reception 9:00 – 9:05am Roger Melko, Perimeter Institute & University of WaterlooWelcome and Opening Remarks Bob Room Morning Chair: Miles Stoudenmire, Perimeter Institute 9:05 – 9:45am David Hawthorn, University of WaterlooCharge density wave order in cuprate superconductors Bob Room 9:45 – 10:30am Zlatko Papic, Perimeter InstituteTopological phases in graphene Bob Room 10:30 – 11:00am Break Bistro – 1st Floor 11:00 – 11:45am Luiz Santos, Perimeter InstituteAharonov-Bohm effect in symmetry protected states Bob Room 11:45 – 12:30pm Zheng-Cheng Gu, Perimeter InstituteEmergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:00pm Free Discussions 3:00 – 3:30pm Break Bistro – 1st Floor 3:30 – 5:00pm Free Discussions

Tuesday, February 11, 2014

 Time Event Location Morning Chair: William Witczak-Krempa, Perimeter Institute 9:00 – 9:45am Jan Kycia, University of WaterlooSpecific heat and ac susceptibility measurements on the Spin Ice, Dy2Ti2O7 Bob Room 9:45 – 10:30am Anton Burkov, University of WaterlooTopological response in gapless systems:from Weyl semimetals to metallic ferromagnets Bob Room 10:30 – 11:00am Break Bistro – 1st Floor 11:00 – 11:45am Arun Paramekanti, University of TorontoTuning magnetism and Chern bands in spin-orbit coupled double perovskites Bob Room 11:45 – 12:30pm Pavel Wiegmann, University of ChicagoFractional Quantum Hall Effect in a curved space Bob Room 12:30 – 12:35pm Conference Photo TBA 12:35 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:00pm Free Discussions 3:00 – 3:30pm Break Bistro – 1st Floor 3:30 – 5:00pm Free Discussions

Wednesday, February 12, 2014

 Time Event Location Morning Chair: Juan Carrasquillia, Perimeter Institute 9:00 – 9:45am Duncan Haldane, Princeton UniversityGeometry of topological matter: some examples Bob Room 9:45 – 10:30am Dmitry Abanin, Perimeter InstituteMany-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics Bob Room 10:30 – 11:00am Break Bistro – 1st Floor 11:00 – 11:45am Paul Fendley, University of VirginiaGeometrical dependence of information in 2d critical systems Bob Room 11:45 – 12:30pm Max Metlitski, University of California, Santa BarbaraA symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators. Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:30pm Colloquium:  Matthew Fisher,University of California, Santa BarbaraQuantum Tapestries Theater 3:30 – 4:00pm Break Bistro – 1st Floor 4:00 – 5:00pm Free Discussions 5:30pm Banquet Bistro – 2nd Floor

Thursday, February 13, 2014

 Time Event Location Morning Chair: Ipsita Mandal, Perimeter Institute 9:00 – 9:45am Guifre Vidal, Perimeter Institute &Lukasz Cincio, Perimeter InstituteChiral spin liquid and emergent anyons in a Kagome lattice Mott insulator Bob Room 9:45 – 10:30am Senthil Todari, Massachusetts Institute of TechnologyInteracting electronic topological insulators in three dimensions Bob Room 10:30 – 11:00am Break Bistro – 1st Floor 11:00 – 11:45am Brian Swingle, Harvard UniversityIncoherent metals Bob Room 11:45 – 12:30pm Zhenghan Wang, Microsoft Station QGauging symmetry of 2D topological phases Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:00pm Free Discussions 3:00 – 3:30pm Break Bistro – 1st Floor 4:00 – 5:00pm Colloquium:  Subir Sachdev, Harvard UniversityQuantum criticality and high temperature superconductivity University of WaterlooPHY 150 5:00pm Pub Night Bistro

Friday, February 14, 2014

 Time Event Location Morning Chair: Peng Ye, Perimeter Institute 9:00 – 9:45am Anushya Chandran, Perimeter InstituteHow universal is the entanglement spectrum? Bob Room 9:45 – 10:30am Yuan-Ming Lu, University of California, BerkeleyA unification of symmetric Z2 spin liquids on kagome lattice Bob Room 10:30 – 11:00am Break Bistro – 1st Floor 11:00 – 11:45am Ganapathy Baskaran,The Institute of Mathematical Sciences ChennaiLow Spin State Mott Insulators and Emergence of novel Quantum Spin Liquids Bob Room 11:45 – 12:30pm Chris Laumann, Princeton UniversityMany-body localization with dipoles Bob Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:00pm Free Discussions 3:00 – 3:30pm Break Bistro – 1st Floor 3:30 – 5:00pm Free Discussions

Dmitry Abanin, Perimeter Institute

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

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)

Ganapathy Baskaran, The Institute of Mathematical Sciences Chennai

Low Spin State Mott Insulators and Emergence of novel Quantum Spin Liquids

In a conventional Mott insulator, magnitude of local spin moments remain fixed. They are fixed spin Mott insulators'. We suggest that, in a multi orbital Hubbard model, when local Hund coupling is won over by inter-orbital superexchange couplings between neighboring sites, local spin moment can decrease its value in a cooperative fashion, through a first order phase transition, These are Low spin state Mott insulators' (LSSMI). The minimal value of spins that can be reached are zero (half), for even (odd) number of electrons per site, We show that in LSSMI, depending on orbital degeneracy and electron number per site, novel quantum spin liquids can emerge, We discuss systems such as Fe arsenide, Fe selenide family and La2CoO3 in the light of our proposal. Certain long standing puzzles, including absence of any magnetic phase transition in La2CoO3 is explained in terms of a novel quantum spin liquid. Some properties of this spin liquid, a liquid of quantum strings' will be discussed and some predictions made.

Anton Burkov, University of Waterloo

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

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.

Anushya Chandran, Perimeter Institute

How universal is the entanglement spectrum?

It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this talk, I will present evidence to the contrary. I will show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the ES and the Renyi entropies can mislead entirely, while for quantum Hall systems the ES has much less universal content than assumed to date. I will also discuss the consequences of the eigenstate thermalization hypothesis for the entanglement Hamiltonian, showing that a pure state in a sub-system can capture the properties of the reduced density matrix.

Paul Fendley, University of Virginia

Geometrical dependence of information in 2d critical systems

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.

Matthew Fisher, University of California, Santa Barbara

Colloquium:  Quantum Tapestries

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.

Zheng-Cheng Gu, Perimeter Institute

Emergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice

In this talk, I will show the emergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice, from both state-of-art Grassmann tensor-network numerical approach and quantum field theory approach.

Duncan Haldane, Princeton University

Geometry of topological matter: some examples

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 anomalousHall 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

David Hawthorn, University of Waterloo

Charge density wave order in cuprate superconductors

Despite over 25 years of intensive research, the problem of cuprate high temperature superconductors remains unsolved.  One aspect that makes understanding the cuprates difficult is that the superconducting phase competes with other phases of matter, in particular a charge density wave (CDW) state – a spontaneous, spatial modulation of the charge density. It is now clear that understanding the CDW state is of central importance to understanding many aspects of the cuprates.  Recently, breakthroughs in the investigation of CDW order and superconductivity in the cuprates have occurred using a novel experimental technique, resonant soft x-ray scattering.  In this talk, I will discuss experimental investigations of the CDW in the cuprates using resonant x-ray scattering.   These experiments provide key insights into the doping phase diagram of CDW order, the microscopic character of the CDW order and the nature of the competition between CDW and superconducting order parameters, which we argue are intertwined in a multi-dimensional order parameter that experiences thermal angular fluctuations in the pseudogap phase.

Jan Kycia, University of Waterloo

Specific heat and ac susceptibility measurements on the Spin Ice, Dy2Ti2O7

Some time ago (1999), Dy2Ti2O7, was shown to be a magnetic analog of water ice, and thus dubbed "spin ice". Recently, theories and experiments have developed the  perspective of viewing excitations within the low temperature phase of this spin ice as monopoles. I will present early results of specific heat, ac susceptibility and magnetization measurements as well as my group's recent  results on this system

Chris Laumann, Princeton University

Many-body localization with dipoles

Statistical mechanics is the framework that connects thermodynamics to the microscopic world. It hinges on the assumption of equilibration; when equilibration fails, so does much of our understanding. In isolated quantum systems, this breakdown is captured by the phenomenon known as many-body localization. This breakdown manifests in a variety of ways, as elucidated by much recent theoretical and numerical work. Many-body localized phases violate Ohm's law  and Fourier's law as they conduct neither charge nor heat; they can exhibit symmetry breaking and/or topological orders in dimensions normally forbidden by Mermin-Wagner arguments; they hold potential as strongly interacting quantum computers due to the slow decay of local coherence.
In this talk, I will briefly introduce the basic phenomena of many-body localization and review its theoretical status. To date, none of these phenomena has been observed in an experimental system, in part because of the isolation required to avoid thermalization. I will consider several dipolar systems which we believe to be ideal platforms for the realization of MBL phases and for investigating the associated delocalization phase transition. The presence of strong interactions in these systems underlies their potential for exploring physics beyond that of single particle Anderson localization. However, the power law of the dipolar interaction immediately raises the question: can localization in real space persist in the presence of such long-range interactions?
I will review and extend several arguments producing criteria for localization in the presence of power laws and present small-scale numerics regarding the MBL transition in several of the proposed dipolar systems.
Associated preprint:
N. Yao, CRL, S. Gopalakrishnan, M. Knap, M. Mueller, E. Demler., M. Lukin arXiv:1311.7151

Yuan-Ming Lu, University of California, Berkeley

A unification of symmetric Z2 spin liquids on kagome lattice

While there is mounting numerical evidence for a gapped Z2 spin liquid in the kagome Heisenberg model, a complete characterization of this topological phase remains to be accomplished. A defining property, the projective symmetry group (PSG) which fixes how the emergent excitations of the spin liquid phase transform under symmetry, remains to be determined. Following a Chern-Simons field theory, we show how PSG determines measurable properties of a Z2 spin liquid, such as the existence of symmetry protected gapless edge states. This fact enables us to unify two distinct types of projected wavefunctions for Z2 spin liquids: the Schwinger-boson states and the fermionic spinon states. We also provide concrete predictions for identifying the spin liquid ground state on the kagome lattice.

Max Metlitski, University of California, Santa Barbara

A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators

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.

Are non-Fermi-liquids stable to pairing?

States of matter with a sharp Fermi-surface but no well-defined Landau quasiparticles are expected to arise in a number of physical systems. Examples include i) quantum critical points associated with the onset of order in metals, ii) the spinon Fermi-surface (U(1) spin-liquid) state of a Mott insulator and iii) the Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this talk, I will use renormalization group techniques to investigate possible instabilities of such non-Fermi-liquids to pairing. I will show that for a large class of phase transitions in metals, the attractive interaction mediated by order parameter fluctuations always leads to a superconducting instability, which preempts the non-Fermi-liquid effects. On the other hand, the spinon Fermi-surface and the Halperin-Lee-Read states are stable against pairing for a sufficiently weak attractive short-range interaction. However, once the strength of attraction exceeds a critical value, pairing sets in. I will describe the ensuing quantum phase transition between i) the U(1) and the Z_2 spin-liquid states, and ii) the Halperin-Lee-Read and Moore-Read states.

Zlatko Papic, Perimeter Institute

Topological phases in graphene

As realized for the first time in 1980s, quantum many-body systems  in reduced spatial dimensions can sometimes undergo a special type of ordering which does not break any symmetry but introduces long-range entanglement and emergent excitations that have radically different properties from their original constituents. Most of our experimental knowledge of such topological" phases of matter comes from studies of two-dimensional electron gases in GaAs semiconductors in high magnetic fields and at low temperatures. In the first part of this talk, I will give an introduction to these systems and review some latest theoretical developments related to their entanglement properties. In the second part, I will discuss new possibilities for experimental realizations of topological phases in bilayer graphene.  I will present evidence that this material supports an even-denominator" fractional state,  related to the Moore-Read state, whose observation has recently been reported. Finally, I will outline several proposals based on the tunability of the electron-electron interactions in bilayer graphene which might enable further experimental progress beyond GaAs.

Arun Paramekanti, University of Toronto

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

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.

Luiz Santos, Perimeter Institute

Aharonov-Bohm effect in symmetry protected states

Symmetry protected topological (SPT) states are generalizations of topological band insulators to interacting systems. They possess a gapped bulk spectrum together with symmetry protected edge states, with no topological order. There has been recently an intense effort to classify SPT states both in terms of group cohomology as well as from the point of view of effective field theories. An interesting related question is to understand the structute of lattice models that realize SPT physics. In this talk, I shall present a class of lattice models describing the egde of non-chiral two-dimensional bosonic SPT states protected by Z_N symmetry. A crucial aspect of the construction relies on finding the correct non-trivial Z_N symmetry realizations on the edge consistent with all the possible classes of SPT states. Then I shall discuss the Aharonov-Bohm effect on the many-body SPT state by studying this many-body effect on the aforementioned gapless edge states. The effect of a Z_N gauge flux on the egde states is formulated in terms of twisted boundary conditions of the lattice models. The low energy spectral shifts due to the gauge flux are shown to depend on each of the SPT classes in a predictable way. I shall, in the course of this talk, present numerical results of exact diagonalization of our lattice Hamiltonians that support this analysis. This work is done in collaboration with Juven Wang and appears in arXiv:1310.8291.

Brian Swingle, Harvard University

Incoherent metals

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.

Senthil Todadri, Massachusetts Institute of Technology

Interacting electronic topological insulators in three dimensions

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.

Guifre Vidal, Perimeter Institute & Lukasc Cincio, Perimeter Institute

Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator

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.

Zhenghan Wang, Microsoft Station Q

Gauging symmetry of 2D topological phases

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

Pavel Wiegmann, University of Chicago

Fractional Quantum Hall Effect in a curved space

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 responce functions.   The talk is based on the recent paper with T. Can and M. Laskin.

## Many-body localization with dipoles

Vendredi fév 14, 2014
Speaker(s):

Statistical mechanics is the framework that connects thermodynamics to the microscopic world. It hinges on the assumption of equilibration; when equilibration fails, so does much of our understanding. In isolated quantum systems, this breakdown is captured by the phenomenon known as many-body localization. This breakdown manifests in a variety of ways, as elucidated by much recent theoretical and numerical work.

Collection/Series:

## Low Spin State Mott Insulators and Emergence of novel Quantum Spin Liquids

Vendredi fév 14, 2014
Speaker(s):

In a conventional Mott insulator, magnitude of local spin moments remain fixed. They are fixed spin Mott insulators'. We suggest that, in a multi orbital Hubbard model, when local Hund coupling is won over by inter-orbital superexchange couplings between neighboring sites, local spin moment can decrease its value in a cooperative fashion, through a first order phase transition, These are `Low spin state Mott insulators' (LSSMI).

Collection/Series:

## A unification of symmetric Z2 spin liquids on kagome lattice

Vendredi fév 14, 2014
Speaker(s):

While there is mounting numerical evidence for a gapped Z2 spin liquid in the kagome Heisenberg model, a complete characterization of this topological phase remains to be accomplished. A defining property, the projective symmetry group (PSG) which fixes how the emergent excitations of the spin liquid phase transform under symmetry, remains to be determined. Following a Chern-Simons field theory, we show how PSG determines measurable properties of a Z2 spin liquid, such as the existence of symmetry protected gapless edge states.

Collection/Series:

## How universal is the entanglement spectrum?

Vendredi fév 14, 2014
Speaker(s):

It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this talk, I will present evidence to the contrary. I will show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low energy spectrum exhibit singular changes, even when the physical system remains in the same phase.

Collection/Series:

## Are non-Fermi-liquids stable to pairing?

Jeudi fév 13, 2014
Speaker(s):

States of matter with a sharp Fermi-surface but no well-defined Landau
quasiparticles are expected to arise in a number of physical systems.
Examples include i) quantum critical points associated with the onset
of order in metals, ii) the spinon Fermi-surface (U(1) spin-liquid)
state of a Mott insulator and iii) the Halperin-Lee-Read composite
fermion charge liquid state of a half-filled Landau level. In this
talk, I will use renormalization group techniques to investigate

Collection/Series:

## Gauging symmetry of 2D topological phases

Jeudi fév 13, 2014
Speaker(s):

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

Collection/Series:

## Incoherent metals

Jeudi fév 13, 2014
Speaker(s):

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.

Collection/Series:

## Interacting electronic topological insulators in three dimensions

Jeudi fév 13, 2014
Speaker(s):

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.

Collection/Series:

## Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator

Jeudi fév 13, 2014
Speaker(s):

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.

Collection/Series:

## Quantum Tapestries

Mercredi fév 12, 2014
Speaker(s):

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.

Collection/Series:

## Pages

Scientific Organizer:

Roger Melko, Perimeter Institute & University of Waterloo