PI-UIUC 2013

11 talks

November 07, 2013 - November 08, 2013

C13035

Collection Type Conference/School

Description PI-UIUC Joint Workshop On Strongly Correlated Quantum Many-Body Systems

Displaying 1 - 11 of 11

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

Philip Kim Columbia University

November 07, 2013 PIRSA:13110070
Unparticles and Fermi Arcs in the Cuprates

Philip Phillips University of Illinois System

November 07, 2013 PIRSA:13100131
Entanglement at strongly-interacting quantum critical points

Roger Melko University of Waterloo

November 07, 2013 PIRSA:13110071
Topological Phases in Transition Metal Oxides

Gregory Fiete

November 07, 2013 PIRSA:13110072
Many-body localization: entanglement, emergent conservation laws, and the structure of eigenstates

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

November 07, 2013 PIRSA:13110073
Quantum quenches & holography

Robert Myers Perimeter Institute for Theoretical Physics

November 07, 2013 PIRSA:13110074
Discussion

Eduardo Fradkin University of Illinois System

November 07, 2013 PIRSA:13110075
Majorana State Properties in Semiconductor and Oxide Superconducting Quantum Wires

Allan MacDonald The University of Texas at Austin

November 08, 2013 PIRSA:13110076
Quantum and Classical Anomalies

Michael Stone University of Illinois System

November 08, 2013 PIRSA:13110077
Twist Defects in Topological Systems with Anyonic Symmetries

Jeffrey Teo University of Illinois System

November 08, 2013 PIRSA:13110078
Discussion

Xiao-Gang Wen Massachusetts Institute of Technology (MIT) - Department of Physics

November 08, 2013 PIRSA:13110079

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

Philip Kim Columbia University

November 07, 2013 PIRSA:13110070

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.
Unparticles and Fermi Arcs in the Cuprates

Philip Phillips University of Illinois System

November 07, 2013 PIRSA:13100131

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.
Entanglement at strongly-interacting quantum critical points

Roger Melko University of Waterloo

November 07, 2013 PIRSA:13110071

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.
Topological Phases in Transition Metal Oxides

Gregory Fiete

November 07, 2013 PIRSA:13110072

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

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

November 07, 2013 PIRSA:13110073
Quantum quenches & holography

Robert Myers Perimeter Institute for Theoretical Physics

November 07, 2013 PIRSA:13110074

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.
Discussion

Eduardo Fradkin University of Illinois System

November 07, 2013 PIRSA:13110075
Majorana State Properties in Semiconductor and Oxide Superconducting Quantum Wires

Allan MacDonald The University of Texas at Austin

November 08, 2013 PIRSA:13110076

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.
Quantum and Classical Anomalies

Michael Stone University of Illinois System

November 08, 2013 PIRSA:13110077

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.
Twist Defects in Topological Systems with Anyonic Symmetries

Jeffrey Teo University of Illinois System

November 08, 2013 PIRSA:13110078

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.
Discussion

Xiao-Gang Wen Massachusetts Institute of Technology (MIT) - Department of Physics

November 08, 2013 PIRSA:13110079

Title	Speaker(s)	Date	Talk Type	Info
Hofstadter’s Butterfly and interaction driven quantum Hall ferromagnetism in graphene	Philip Kim	2013-11-07	Conference	View details
Unparticles and Fermi Arcs in the Cuprates	Philip Phillips	2013-11-07	Conference	View details
Entanglement at strongly-interacting quantum critical points	Roger Melko	2013-11-07	Conference	View details
Topological Phases in Transition Metal Oxides	Gregory Fiete	2013-11-07	Conference	View details
Many-body localization: entanglement, emergent conservation laws, and the structure of eigenstates	Dmitry Abanin	2013-11-07	Conference	View details
Quantum quenches & holography	Robert Myers	2013-11-07	Conference	View details
Discussion	Eduardo Fradkin	2013-11-07	Conference	View details
Majorana State Properties in Semiconductor and Oxide Superconducting Quantum Wires	Allan MacDonald	2013-11-08	Conference	View details
Quantum and Classical Anomalies	Michael Stone	2013-11-08	Conference	View details
Twist Defects in Topological Systems with Anyonic Symmetries	Jeffrey Teo	2013-11-08	Conference	View details
Discussion	Xiao-Gang Wen	2013-11-08	Conference	View details

PI-UIUC 2013

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