Emergence in Complex Systems

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
Interacting electronic topological insulators in three dimensions

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

February 13, 2014

PIRSA:14020123
Incoherent metals

Brian Swingle
Brandeis University

February 13, 2014

PIRSA:14020124
Gauging symmetry of 2D topological phases

Zhenghan Wang
Microsoft Corporation

February 13, 2014

PIRSA:14020125
Are non-Fermi-liquids stable to pairing?

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

February 13, 2014

PIRSA:14020143
How universal is the entanglement spectrum?

Anushya Chandran
Perimeter Institute for Theoretical Physics

February 14, 2014

PIRSA:14020132
A unification of symmetric Z2 spin liquids on kagome lattice

Yuan-Ming Lu

February 14, 2014

PIRSA:14020118
Low Spin State Mott Insulators and Emergence of novel Quantum Spin Liquids

Baskaran Ganapathy
Institute of Mathematical Sciences

February 14, 2014

PIRSA:14020128
Many-body localization with dipoles

Chris Laumann
Boston University

February 14, 2014

PIRSA:14020129

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

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

February 13, 2014

PIRSA:14020143

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.
How universal is the entanglement spectrum?

Anushya Chandran
Perimeter Institute for Theoretical Physics

February 14, 2014

PIRSA:14020132

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.
A unification of symmetric Z2 spin liquids on kagome lattice

Yuan-Ming Lu

February 14, 2014

PIRSA:14020118

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

Baskaran Ganapathy
Institute of Mathematical Sciences

February 14, 2014

PIRSA:14020128

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.
Many-body localization with dipoles

Chris Laumann
Boston University

February 14, 2014

PIRSA:14020129

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

Title	Speaker(s)	Date	Talk Type	Info
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator	Guifre Vidal, Lukasz Cincio	2014-02-13	Conference	View details
Interacting electronic topological insulators in three dimensions	Senthil Todadri	2014-02-13	Conference	View details
Incoherent metals	Brian Swingle	2014-02-13	Conference	View details
Gauging symmetry of 2D topological phases	Zhenghan Wang	2014-02-13	Conference	View details
Are non-Fermi-liquids stable to pairing?	Max Metlitski	2014-02-13	Conference	View details
How universal is the entanglement spectrum?	Anushya Chandran	2014-02-14	Conference	View details
A unification of symmetric Z2 spin liquids on kagome lattice	Yuan-Ming Lu	2014-02-14	Conference	View details
Low Spin State Mott Insulators and Emergence of novel Quantum Spin Liquids	Baskaran Ganapathy	2014-02-14	Conference	View details
Many-body localization with dipoles	Chris Laumann	2014-02-14	Conference	View details

Emergence in Complex Systems

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