PI-UIUC Joint Workshop on Strongly Correlated Quantum Many-Body Systems

Conference Date: 
Jeudi, Novembre 7, 2013 (All day) to Vendredi, Novembre 8, 2013 (All day)
Pirsa Collection: 
Scientific Areas: 
Condensed Matter

The main purpose of this workshop is to exchange new ideas in strongly correlated electron systems and promote collaborations among researchers at the Perimeter Institute and the University of Illionis at Urbana-Champaign.

Last year, the first joint workshop between the two institutes was held at Urbana-Champaign with focus on topological quantum matter, application of holographic methods in condensed matter physics and Majorana fermions.

This year, Perimeter Institute plans to host the second joint workshop. The topics to be discussed in the workshop include the interplay between symmetry and topology in quantum many-body systems, entanglement in numerical simulations and experiments, quantum phase transitions and criticality. 

  • Dima Abanin, Perimeter Institute
  • Gregory Fiete, University of Texas
  • Eduardo Fradkin, University of Illinois
  • Philip Kim, Columbia University
  • Allan MacDonald, University of Texas
  • Roger Melko, Perimeter Institute & University of Waterloo
  • Robert Myers, Perimeter Institute
  • Philip Philips, University of Illinois
  • Michael Stone, University of Illinois
  • Jeffrey Teo, Univesity of Illinois
  • Xiao-Gang Wen, Perimeter Institute
  • Dima Abanin, Perimeter Institute
  • Ganapathy Baskaran, The Institute of Mathematical Sciences Chennai
  • John Berlinsky, Perimeter Institute
  • Pablo Bueno, Instituto de Física Teórica 
  • Hitesh Changlani, University of Illinois
  • Gil Cho, University of Illinois
  • Denis Dalidovich, Perimeter Institute
  • Gregory Fiete, University of Texas
  • Eduardo Fradkin, University of Illinois
  • Taylor Hughes, University of Illinois
  • Ann Kallin, University of Waterloo
  • Catherine Kallin, McMaster University
  • Philip Kim, Columbia University
  • Keith Lee, Perimeter Institute
  • Sung-Sik Lee, Perimeter Institute & McMaster University
  • Rob Leigh, University of Illinois
  • Allan MacDonald, University of Texas
  • Roger Melko, Perimeter Institute & University of Waterloo
  • Robert Myers, Perimeter Institute
  • Tami Pereg-Barnea, McGill University
  • Philip Philips, University of Illinois
  • Shinsei Ryu, University of Illinois
  • Vasudha Shivamoggi, University of Illinois
  • Michael Stone, University of Illinois
  • Evelyn Tang, Massachusetts Institute of Technology
  • Jeffrey Teo, Univesity of Illinois
  • Erik Tonni, SISSA
  • Norm Tubman, University of Illinois
  • Guifre Vidal, Perimeter Institute
  • Smitha Vishveshwara, University of Illinois
  • Xiao-Gang Wen, Perimeter Institute

Thursday, November 7, 2013

Time

Event

Location

8:30 – 9:00am

Registration

Reception

9:00 – 9:05am

Organizers
Welcome and Opening Remarks

Bob Room

9:05 – 10:05am

Philip Kim, Columbia University
Hofstadter’s Butterfly and interaction driven quantum
Hall ferromagnetism in graphene

Bob Room

10:05 – 10:45am

Break

Bistro – 1st Floor

10:45 – 11:30am

Philip Philips, University of Illinois
Unparticles and Fermi Arcs in the Cuprates

Bob Room

11:30 – 12:15pm

Roger Melko, Perimeter Institute & University of Waterloo
Entanglement at strongly-interacting quantum critical points

Bob Room

12:15 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:00pm

Greg Fiete, University of Texas
Topological Phases in Transition Metal Oxides

Bob Room

3:00 – 3:45pm

Dmitry Abanin, Perimeter Institute
Many-body localization: entanglement, emergent conservation laws, and the structure of eigenstates

Bob Room

3:45 – 4:15pm

Break

Bistro – 1st Floor

4:15 – 5:00pm

Robert Myers, Perimeter Institute
Quantum quenches & holography

Bob Room

5:00 – 6:00pm

Eduardo Fradkin, University of Illinois
(discussion)

Bob Room

6:00pm

Banquet

Bistro – 2nd Floor

 

Friday, November 8, 2013

Time

Event

Location

9:00 – 10:00am

Allan MacDonald, University of Texas
Majorana State Properties in Semiconductor and
Oxide Superconducting Quantum Wires

Bob Room

10:00 – 10:05am

Conference Photo

TBA

10:05 – 10:30am

Break

Bistro – 1st Floor

10:30 - 11:15am

Michael Stone, University of Illinois
Quantum and Classical Anomalies

Bob Room

11:15 – 12:00pm

Jeffrey Teo, University of Illinois
Twist Defects in Topological Systems
with Anyonic Symmetries

Bob Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:00pm

Xiao-Gang Wen, Perimeter Institute
(discussion)

Bob Room

 

 

Dima Abanin, Perimeter Institute

Many-body localization: entanglement, emergent conservation laws, and the structure of eigenstates 

Gregory Fiete, University of Texas

Topological Phases in Transition Metal Oxides

Certain varieties of transition metal oxides possess both significant interactions and strong spin-orbit coupling. In this talk I will describe materials-motivated models that predict topological phases in heterostructured and bulk transition metal oxides. We find Z2 topological insulators, Chern insulators, topological crystalline insulators, and interaction-driven topological phases not adiabatically connected to non-interacting topological phases. 

Philip Kim, Columbia University

Hofstadter’s Butterfly and interaction driven quantum Hall ferromagnetism in graphene

Electrons moving in a periodic electric potential form Bloch energy bands where the mass of electrons are effectively changed. In a strong magnetic field, the cyclotron orbits of free electrons are quantized and Landau levels forms with a massive degeneracy within. In 1976, Hofstadter showed that for 2-dimensional electronic system, the intriguing interplay between these two quantization effects can lead into a self-similar fractal set of energy spectrum known as “Hofstadter’s Butterfly.” Experimental efforts to demonstrate this fascinating electron energy spectrum have continued ever since. Recent advent of graphene, where its Bloch electrons can be described by Dirac feremions, provides a new opportunity to investigate this half century old problem experimentally. In this presentation, I will discuss the experimental realization Hofstadter’s Butterfly via substrate engineered graphene under extremely high magnetic fields controlling two competing length scales governing Dirac-Bloch states and Landau orbits, respectively. In addition, the strong Coulomb interactions and approximate spin-pseudo spin symmetry are predicted to lead to a variety of integer quantum Hall ferromagnetic and fractional quantum Hall states and the quantum phase transition between them in graphene. I will discuss several recent experimental evidences to demonstrate the role of the electron interaction in single and bilayer graphene. 

Allan MacDonald, University of Texas

Majorana State Properties in Semiconductor and Oxide Superconducting Quantum Wires

When proximity coupled to s-wave superconductors, quantum wires can support effective p-wave superconductivity under appropriate circumstances.  The p-wave state has  Majorana states at the wire ends which can store quantum information.  I will discuss some properties of Majorana states formed in oxide and semiconductor quantum wires, including superconducting state phase diagrams as a function of spin-orbit coupling strength, Fermi energy, and external magnetic field strength, and Majorana exchange properties. 

Roger Melko, Perimeter Institute & University of Waterloo

Entanglement at strongly-interacting quantum critical points

At a quantum critical point (QCP) in two or more spatial dimensions, leading-order contributions to the scaling of entanglement entropy typically follow the "area" law, while sub-leading behavior contains universal physics.  Different universal functions can be access through entangling subregions of different geometries.  For example, for polygonal shaped subregions, quantum field theories have demonstrated that the sub-leading scaling is logarithmic, with a universal coefficient dependent on the number of vertices in the polygon.  Although such universal quantities are routinely studied in non-interacting field theories, it requires numerical simulation to access them in interacting theories.  In this talk, we discuss numerical calculations of the Renyi entropies at QCPs in 2D quantum lattice models.  We calculate the universal coefficient of the vertex-induced logarithmic scaling term, and compare to non-interacting field theory calculations.  Also, we examine the shape dependence of the Renyi entropy for finite-size lattices with smooth subregion boundaries. Such geometries provide a sensitive probe of the gapless wavefunction in the thermodynamic limit, and give new universal quantities that could be examined by field-theoretical studies in 2+1D.

Robert Myers, Perimeter Institute

Quantum quenches & holography

We employ holographic techniques to study quantum quenches at finite temperature, where the quenches involve varying the coupling of the boundary theory to a relevant operator with an arbitrary conformal dimension. The evolution of the system is studied by evaluating the expectation value of the quenched operator and the stress tensor throughout the process. The time dependence of the new coupling is characterized by a fixed timescale and the response of the observables depends on the ratio of the this timescale to the initial temperature. The observables exhibit universal scaling behaviours when the transitions are either fast or slow, i.e., when this ratio is very small or very large. For fast quenches, we uncover a universal scaling behaviour in the response of the system, which depends only on the conformal dimension of the quenched operator in the vicinity of the ultraviolet fixed point of the theory. 

Philip Philips, University of Illinois

Unparticles and Fermi Arcs in the Cuprates

One of the open problems in strong correlation physics is whether or not Luttinger's theorem works for doped Mott insulators, particularly in the pseudo gap regime where the pole-like excitations form only a Fermi arc. I will begin this talk by using this theorem to count particles and show that it fails in general for the Mott state. The failure stems from the divergent self energy that underlies Mottness. When such a divergence is present, charged degrees of freedom are present that have no particle interpretation. I will argue that such excitations are governed by a non-trivial IR fixed point and the propagator of which is of the unparticle form proposed by Georgi. I will show how a gravity dual can be used to determine the scaling dimension of the unparticle propagator. I will close by elucidating a possible superconducting instability of unparticles and demonstrate that unparticle stuff is likely to display fractional statistics in the dimensionalities of interest for strongly correlated electron matter.  Time permitting, an underlying theory of the strongly coupled fixed point will be outlined.

Michael Stone, University of Illinois

Quantum and Classical Anomalies

I will begin reviewing the Callan-Harvey mechanism of anomaly inflow with particular focus on topological edge states and show how the  inflow  picture naturally converts the non-covariant  "consistent" gauge anomaly  of Bardeen and Zumino to the more physical "covariant" anomaly. I will then  discuss some recent  derivations of the covariant form of the gauge anomaly from classical phase space flows.

Jeffrey Teo, University of Illinois

Twist Defects in Topological Systems with Anyonic Symmetries

Twist defects are point-like objects that support robust non-local storage of quantum information and non-abelian unitary operations. Unlike quantum deconfined anyonic excitations, they rely on symmetry rather than a non-abelian topological order. Zero energy Majorana bound states can arise at lattice defects, such as disclinations and dislocations, in a topological crystalline superconductor. More general parafermion bound state can appear as twist defects in a topological phase with an anyonic symmetry, such as a bilayer fractional quantum Hall state and the Kitaev toric code. They are however fundamentally different from quantum anyonic excitations in a true topological phase. This is demonstrated by their unconventional exchange and braiding behavior, which is characterized by a modified spin statistics theorem and modular invariance.

 

 

Vendredi nov 08, 2013
Speaker(s): 
Collection/Series: 

 

Vendredi nov 08, 2013
Speaker(s): 

Twist defects are point-like objects that support robust non-local
storage of quantum information and non-abelian unitary operations.
Unlike quantum deconfined anyonic excitations, they rely on symmetry
rather than a non-abelian topological order. Zero energy Majorana bound
states can arise at lattice defects, such as disclinations and
dislocations, in a topological crystalline superconductor. More general
parafermion bound state can appear as twist defects in a topological

Collection/Series: 

 

Vendredi nov 08, 2013
Speaker(s): 

I will begin reviewing the Callan-Harvey mechanism of anomaly inflow
with particular focus on topological edge states and show how the
 inflow  picture naturally converts the non-covariant  "consistent"
gauge anomaly  of Bardeen and Zumino to the more physical "covariant"
anomaly. I will then  discuss some recent  derivations of the covariant
form of the gauge anomaly from classical phase space flows.

Collection/Series: 

 

Vendredi nov 08, 2013

When proximity coupled to s-wave superconductors, quantum wires can
support effective p-wave superconductivity under appropriate
circumstances.  The p-wave state has  Majorana states at the wire ends
which can store quantum information.  I will discuss some properties of
Majorana states formed in oxide and semiconductor quantum wires,
including superconducting state phase diagrams as a function of
spin-orbit coupling strength, Fermi energy, and external magnetic field
strength, and Majorana exchange properties.

Collection/Series: 

 

Jeudi nov 07, 2013
Speaker(s): 
Collection/Series: 

 

Jeudi nov 07, 2013
Speaker(s): 

We employ holographic techniques to study quantum quenches at finite
temperature, where the quenches involve varying the coupling of the
boundary theory to a relevant operator with an arbitrary conformal
dimension. The evolution of the system is studied by evaluating the
expectation value of the quenched operator and the stress tensor
throughout the process. The time dependence of the new coupling is
characterized by a fixed timescale and the response of the observables

Collection/Series: 

 

Jeudi nov 07, 2013

Certain varieties of transition metal oxides possess both significant
interactions and strong spin-orbit coupling. In this talk I will
describe materials-motivated models that predict topological phases in
heterostructured and bulk transition metal oxides. We find Z2
topological insulators, Chern insulators, topological crystalline
insulators, and interaction-driven topological phases not adiabatically
connected to non-interacting topological phases.

Collection/Series: 

 

Jeudi nov 07, 2013
Speaker(s): 

At a quantum critical point (QCP) in two or more spatial dimensions,
leading-order contributions to the scaling of entanglement entropy
typically follow the "area" law, while sub-leading behavior contains
universal physics.  Different universal functions can be access through
entangling subregions of different geometries.  For example, for
polygonal shaped subregions, quantum field theories have demonstrated
that the sub-leading scaling is logarithmic, with a universal
coefficient dependent on the number of vertices in the polygon. 

Collection/Series: 

 

Jeudi nov 07, 2013

One of the open problems in strong correlation physics is whether or not
Luttinger's theorem works for doped Mott insulators, particularly in
the pseudo gap regime where the pole-like excitations form only a Fermi
arc. I will begin this talk by using this theorem to count particles and
show that it fails in general for the Mott state. The failure stems
from the divergent self energy that underlies Mottness. When such a
divergence is present, charged degrees of freedom are present that have

Collection/Series: 

Pages

Scientific Organizers:

Dima Abanin, Perimeter Institute
John Berlinsky, Perimeter Institute
Sung-Sik Lee, Perimeter Institute & McMaster University