Emergence & Entanglement II 2013

Topological Phases with of Bosons with Short Range Quantum Entanglement

Ashvin Vishwanath
Harvard University
May 10, 2013

PIRSA:13050046
Condensed Matter
Geometry and the entanglement spectrum in the fractional quantum Hall effect.
May 10, 2013

PIRSA:13050049
Condensed Matter
Defects in Topologically Ordered Quantum Matter

Maissam Barkeshli
University of California, Santa Barbara
May 10, 2013

PIRSA:13050053
Condensed Matter
Twisted Symmetry in Tensor Network States and Topological Order

Oliver Buerschaper
Multiverse Computing (Germany)
May 10, 2013

PIRSA:13050048
Quantum Information

Condensed Matter
Momentum polarization: an entanglement measure of topological spin and chiral central charge

Xiaoliang Qi
Stanford University
May 10, 2013

PIRSA:13050047
Condensed Matter
A gauge theory generalization of the fermion-doubling theorem

John McGreevy
University of California, San Diego
May 10, 2013

PIRSA:13050050
Quantum Fields and Strings

Condensed Matter
Entanglement at strongly-interacting quantum critical points in 2+1D

Roger Melko
University of Waterloo
May 10, 2013

PIRSA:13050051
Quantum Information

Topological Phases with of Bosons with Short Range Quantum Entanglement

Ashvin Vishwanath
Harvard University
May 10, 2013

PIRSA:13050046
Condensed Matter
Geometry and the entanglement spectrum in the fractional quantum Hall effect.
May 10, 2013

PIRSA:13050049
Condensed Matter
Fractional quantum hall states with nu = p/q have a characteristic geometry defined by the electric quadrupole moment of the neutral composite boson that is formed by "flux attachment" of q "flux quanta" (guiding-center orbitals) to p charged particles. This characterizes the "Hall viscosity". For FQHE states described by a conformal field theory with a Euclidean metric g_ab, the quadrupole moment is proportional to the "guiding-center spin" of the composite boson and the inverse metric. The geometry gives rise to dipole moments at external edges or internal "orbital entanglement cuts", and can be seen in the entanglement spectrum.
Defects in Topologically Ordered Quantum Matter

Maissam Barkeshli
University of California, Santa Barbara
May 10, 2013

PIRSA:13050053
Condensed Matter
I will discuss recent advances in our understanding of extrinsic defects in topologically ordered states. These include line defects, where I will discuss recent developments in the classification of gapped boundaries between Abelian topological states, and various kinds of point defects, which host a rich set of topological physics. The extrinsic point defects provide a new way of realizing topologically protected ground state degeneracies, they carry projective non-abelian statistics even in an Abelian topological state and provide a new path towards universal topological quantum computation, they host a general class of topologically protected "parafermion" zero modes, and they provide an avenue towards distinguishing various symmetry-enriched topological phases. I will discuss several novel physical realizations of such point defects, and also a recent experimental proposal to realize such defects in conventional bilayer fractional quantum Hall systems.
Twisted Symmetry in Tensor Network States and Topological Order

Oliver Buerschaper
Multiverse Computing (Germany)
May 10, 2013

PIRSA:13050048
Quantum Information

Condensed Matter
Momentum polarization: an entanglement measure of topological spin and chiral central charge

Xiaoliang Qi
Stanford University
May 10, 2013

PIRSA:13050047
Condensed Matter
Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by . For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge . In this paper we propose a new approach to compute the topological spin and chiral central charge in lattice models by defining a new quantity named as the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a "partial translation operator". We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination of topological spin and central charge. Numerical results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model, and the Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wavefunction. The numerical results verifies the analytic formula with high accuracy, and further suggests that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides a new efficient approach to characterize and identify topological states of matter from finite size numerics.
A gauge theory generalization of the fermion-doubling theorem

John McGreevy
University of California, San Diego
May 10, 2013

PIRSA:13050050
Quantum Fields and Strings

Condensed Matter
This talk is about obstructions to symmetry-preserving regulators of quantum field theories in 3+1 dimensions. New examples of such obstructions can be found using the fact that 4+1-dimensional SPT states are characterized by their edge states.
(Based on work in progress with S.M. Kravec.)
Entanglement at strongly-interacting quantum critical points in 2+1D

Roger Melko
University of Waterloo
May 10, 2013

PIRSA:13050051
Quantum Information
In two or more spatial dimensions, leading-order contributions to the scaling of entanglement entropy typically follow the "area" or boundary law. Although this leading-order scaling is non-universal, at a quantum critical point (QCP), the sub-leading behavior does contain universal physics. Different universal functions can be access through entangling regions of different geometries. For example, for polygonal shaped regions, quantum field theories have demonstrated that the subleading 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 often requires numerical simulation to access them in interacting theories. In this talk, I discuss quantum Monte Carlo (QMC) and numerical Linked-Cluster Expansion (NLCE) calculations of the Renyi entropies at the transverse-field Ising model QCP on the 2D square lattice. We calculate the universal coefficient of the vertex-induced logarithmic scaling term, and compare to non-interacting field theory calculations by Casini and Huerta. Also, we examine the shape dependence of the Renyi entropy for finite-size toroidal lattices with smooth boundaries. Such geometries provide a sensitive probe of the gapless wave function in the thermodynamic limit, and give new universal quantities that could be examined by future field-theoretical studies in 2+1D.

Title	Speaker(s)	Date	Talk Type	Info
Topological Phases with of Bosons with Short Range Quantum Entanglement	Ashvin Vishwanath	2013-05-10	Conference	View details
Geometry and the entanglement spectrum in the fractional quantum Hall effect.		2013-05-10	Conference	View details
Defects in Topologically Ordered Quantum Matter	Maissam Barkeshli	2013-05-10	Conference	View details
Twisted Symmetry in Tensor Network States and Topological Order	Oliver Buerschaper	2013-05-10	Conference	View details
Momentum polarization: an entanglement measure of topological spin and chiral central charge	Xiaoliang Qi	2013-05-10	Conference	View details
A gauge theory generalization of the fermion-doubling theorem	John McGreevy	2013-05-10	Conference	View details
Entanglement at strongly-interacting quantum critical points in 2+1D	Roger Melko	2013-05-10	Conference	View details

Emergence & Entanglement II 2013

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