Conference

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

Xiaoliang Qi Stanford University
May 10, 2013

PIRSA:13050047
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
Defects in Topologically Ordered Quantum Matter

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

PIRSA:13050053
Condensed Matter
Geometry and the entanglement spectrum in the fractional quantum Hall effect.
May 10, 2013

PIRSA:13050049
Condensed Matter
Topological Phases with of Bosons with Short Range Quantum Entanglement

Ashvin Vishwanath Harvard University
May 10, 2013

PIRSA:13050046
Condensed Matter
Spin-orbital quantum liquid on the honeycomb lattice

Philippe Corboz Universiteit van Amsterdam
May 09, 2013

PIRSA:13050045
Quantum Information

Condensed Matter
Characterizing topological spin liquids using PEPS

Norbert Schuch Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
May 09, 2013

PIRSA:13050044
Quantum Information
Emergence and Entanglement in Matrix Product States

Frank Verstraete Ghent University
May 09, 2013

PIRSA:13050043
Quantum Information
Characterizing topological order form a microscopic lattice Hamiltonian

Lukasz Cincio Los Alamos National Laboratory
May 09, 2013

PIRSA:13050042
Quantum Information

Condensed Matter
Directed Influence in the RG Flow

Glen Evenbly Georgia Institute of Technology
May 09, 2013

PIRSA:13050041
Quantum Fields and Strings
Quantum Spin Liquids,Density Matrix Renormalization Group, and Entanglement

Leon Balents University of California, Santa Barbara
May 09, 2013

PIRSA:13050040
Condensed Matter
Searching for Spin Liquids

Steven White University of California, Irvine
May 09, 2013

PIRSA:13050039
Quantum Fields and Strings

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.
Twisted Symmetry in Tensor Network States and Topological Order

Oliver Buerschaper Multiverse Computing (Germany)
May 10, 2013

PIRSA:13050048
Quantum Information

Condensed Matter
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.
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.
Topological Phases with of Bosons with Short Range Quantum Entanglement

Ashvin Vishwanath Harvard University
May 10, 2013

PIRSA:13050046
Condensed Matter
Spin-orbital quantum liquid on the honeycomb lattice

Philippe Corboz Universiteit van Amsterdam
May 09, 2013

PIRSA:13050045
Quantum Information

Condensed Matter
The symmetric Kugel-Khomskii can be seen as a minimal model describing the interactions between spin and orbital degrees of freedom in certain transition-metal oxides with orbital degeneracy, and it is equivalent to the SU(4) Heisenberg model of four-color fermionic atoms. We present simulation results for this model on various two-dimensional lattices obtained with infinite projected-entangled pair states (iPEPS), an efficient variational tensor-network ansatz for two dimensional wave functions in the thermodynamic limit. We find a rich variety of exotic phases: while on the square and checkerboard lattices the ground state exhibits dimer-N\'eel order and plaquette order, respectively, quantum fluctuations on the honeycomb lattice destroy any order, giving rise to a spin-orbital liquid. Our results are supported from flavor-wave theory and exact diagonalization. Furthermore, the properties of the spin-orbital liquid state on the honeycomb lattice are accurately accounted for by a projected variational wave-function based on the pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the ground state is an algebraic spin-orbital liquid. This model provides a possible starting point to understand the recently discovered spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest to choose optical lattices with honeycomb geometry in the search for quantum liquids in ultra-cold four-color fermionic atoms.
Characterizing topological spin liquids using PEPS

Norbert Schuch Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
May 09, 2013

PIRSA:13050044
Quantum Information
Projected Entangled Pair States (PEPS) provide a local description of correlated many-body states. I will discuss how PEPS can be used to characterize topological spin liquids, in particular Resonating Valence Bond states. On the one hand, I will show how the symmetries in the local PEPS description allow to identify that these states appear as topologically degenerate ground states of local Hamiltonians. On the other hand, I will discuss how from exact diagonalization of the transfer operator one can extract both the topological order and the spin liquid nature of the ground state.
Emergence and Entanglement in Matrix Product States

Frank Verstraete Ghent University
May 09, 2013

PIRSA:13050043
Quantum Information
Characterizing topological order form a microscopic lattice Hamiltonian

Lukasz Cincio Los Alamos National Laboratory
May 09, 2013

PIRSA:13050042
Quantum Information

Condensed Matter
In this talk I will show how to obtain a detailed characterization of the emergent topological order starting from microscopic Hamiltonian on a two dimensional lattice. A key step is to obtain a tensor network representation for a complete set of ground states of the Hamiltonian, ﬁrst on an inﬁnite cylinder and then on a ﬁnite torus. As an application of the method I will study lattice Hamiltonians that give rise to selected anyon models, namely chiral semion, Ising as well as Z_3 and Z_5 models.
Directed Influence in the RG Flow

Glen Evenbly Georgia Institute of Technology
May 09, 2013

PIRSA:13050041
Quantum Fields and Strings
Given two lattice Hamiltonians H_1 and H_2 that are identical everywhere except on a local region R of the lattice, we propose a relationship between their ground states psi_1 and psi_2. Specifically, assuming the states can be represented as multi-scale entanglement renormalization ansatz (MERA), we propose a principle of directed influence which asserts that the tensors in the MERA’s that represent the ground states can be chosen to be identical everywhere except within a specific, localized region of the tensor network. The validity of this principle is justified by demonstrating it to follow from Wilson's renormalization ideas towards systems with manifestly separated energy scales. This result is shown, through numerical examples, to have practical applications towards the efficient simulation of systems with impurities, boundaries and interfaces, and also argued to provide useful insights towards holographic representations of quantum states.
Quantum Spin Liquids,Density Matrix Renormalization Group, and Entanglement

Leon Balents University of California, Santa Barbara
May 09, 2013

PIRSA:13050040
Condensed Matter
I will review recent work in our group using Density Matrix Renormalization Group (DMRG) to search for and study quantum spin liquid and topologically ordered states in two dimensional model Hamiltonians. This proves an efficient way to study these phases in semi-realistic situations. I will try to draw lessons from several studies and theoretical considerations.
Searching for Spin Liquids

Steven White University of California, Irvine
May 09, 2013

PIRSA:13050039
Quantum Fields and Strings

Condensed Matter

Title	Speaker(s)	Date	Talk Type	Info link
Momentum polarization: an entanglement measure of topological spin and chiral central charge	Xiaoliang Qi	2013-05-10	Conference	View details
Twisted Symmetry in Tensor Network States and Topological Order	Oliver Buerschaper	2013-05-10	Conference	View details
Defects in Topologically Ordered Quantum Matter	Maissam Barkeshli	2013-05-10	Conference	View details
Geometry and the entanglement spectrum in the fractional quantum Hall effect.		2013-05-10	Conference	View details
Topological Phases with of Bosons with Short Range Quantum Entanglement	Ashvin Vishwanath	2013-05-10	Conference	View details
Spin-orbital quantum liquid on the honeycomb lattice	Philippe Corboz	2013-05-09	Conference	View details
Characterizing topological spin liquids using PEPS	Norbert Schuch	2013-05-09	Conference	View details
Emergence and Entanglement in Matrix Product States	Frank Verstraete	2013-05-09	Conference	View details
Characterizing topological order form a microscopic lattice Hamiltonian	Lukasz Cincio	2013-05-09	Conference	View details
Directed Influence in the RG Flow	Glen Evenbly	2013-05-09	Conference	View details
Quantum Spin Liquids,Density Matrix Renormalization Group, and Entanglement	Leon Balents	2013-05-09	Conference	View details
Searching for Spin Liquids	Steven White	2013-05-09	Conference	View details

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