Emergence in Complex Systems

21 talks

February 10, 2014 - February 14, 2014

C14017

Collection Type

Conference/School

Description

Emergence in Complex Systems

Displaying 1 - 12 of 21

Topological phases in graphene

Zlatko Papic
University of Leeds

February 10, 2014

PIRSA:14020134
Aharonov-Bohm effect in symmetry protected states

Luiz Santos
Emory University

February 10, 2014

PIRSA:14020126
Emergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice

Zheng-Cheng Gu
Chinese University of Hong Kong

February 10, 2014

PIRSA:14020113
Specific heat and ac susceptibility measurements on the Spin Ice, Dy2Ti2O7

Jan Kycia
University of Waterloo

February 11, 2014

PIRSA:14020114
Topological response in gapless systems: from Weyl semimetals to metallic ferromagnets

Anton Burkov
University of Waterloo

February 11, 2014

PIRSA:14020115
Tuning magnetism and Chern bands in spin-orbit coupled double perovskites

Arun Paramekanti
University of Toronto

February 11, 2014

PIRSA:14020116
Fractional Quantum Hall Effect in a curved space

Pavel Wiegmann

February 11, 2014

PIRSA:14020112
Geometry of topological matter: some examples

Duncan Haldane
Princeton University

February 12, 2014

PIRSA:14020117
Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics

Dmitry Abanin

February 12, 2014

PIRSA:14020127
Geometrical dependence of information in 2d critical systems

Paul Fendley
University of Oxford

February 12, 2014

PIRSA:14020119
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators.

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

February 12, 2014

PIRSA:14020120
Quantum Tapestries

Matthew Fisher
University of California, Santa Barbara

February 12, 2014

PIRSA:14020121

Topological phases in graphene

Zlatko Papic
University of Leeds

February 10, 2014

PIRSA:14020134

As realized for the first time in 1980s, quantum many-body systems in reduced spatial dimensions can sometimes undergo a special type of ordering which does not break any symmetry but introduces long-range entanglement and emergent excitations that have radically different properties from their original constituents. Most of our experimental knowledge of such ``topological" phases of matter comes from studies of two-dimensional electron gases in GaAs semiconductors in high magnetic fields and at low temperatures. In the first part of this talk, I will give an introduction to these systems and review some latest theoretical developments related to their entanglement properties. In the second part, I will discuss new possibilities
for experimental realizations of topological phases in bilayer graphene. I will present evidence that this material supports an ``even-denominator" fractional state, related to the Moore-Read state, whose observation has recently been reported. Finally, I will outline several proposals based on the tunability of the electron-electron interactions in bilayer graphene which might enable further experimental progress beyond GaAs.
Aharonov-Bohm effect in symmetry protected states

Luiz Santos
Emory University

February 10, 2014

PIRSA:14020126

Symmetry protected topological (SPT) states are generalizations of topological band insulators to interacting systems. They possess a gapped bulk spectrum together with symmetry protected edge states, with no topological order. There has been recently an intense effort to classify SPT states both in terms of group cohomology as well as from the point of view of effective field theories. An interesting related question is to understand the structute of lattice models that realize SPT physics. In this talk, I shall present a class of lattice models describing the egde of non-chiral two-dimensional bosonic SPT states protected by Z_N symmetry. A crucial aspect of the construction relies on finding the correct non-trivial Z_N symmetry realizations on the edge consistent with all the possible classes of SPT states. Then I shall discuss the Aharonov-Bohm effect on the many-body SPT state by studying this many-body effect on the aforementioned gapless edge states. The effect of a Z_N gauge flux on the egde states is formulated in terms of twisted boundary conditions of the lattice models. The low energy spectral shifts due to the gauge flux are shown to depend on each of the SPT classes in a predictable way. I shall, in the course of this talk, present numerical results of exact diagonalization of our lattice Hamiltonians that support this analysis. This work is done in collaboration with Juven Wang and
appears in arXiv:1310.8291.
Emergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice

Zheng-Cheng Gu
Chinese University of Hong Kong

February 10, 2014

PIRSA:14020113

In this talk, I will show the emergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice, from both state-of-art Grassmann tensor-network numerical approach and quantum field theory approach.
Specific heat and ac susceptibility measurements on the Spin Ice, Dy2Ti2O7

Jan Kycia
University of Waterloo

February 11, 2014

PIRSA:14020114

Some time ago (1999), Dy2Ti2O7, was shown to be a magnetic analog of water ice, and thus dubbed "spin ice". Recently, theories and experiments have developed the perspective of viewing excitations within the low temperature phase of this spin ice as monopoles. I will present early results of specific heat, ac susceptibility and magnetization measurements as well as my group's recent results on this system
Topological response in gapless systems: from Weyl semimetals to metallic ferromagnets

Anton Burkov
University of Waterloo

February 11, 2014

PIRSA:14020115

Standard picture of a topologically-nontrivial phase of matter is an insulator with a bulk energy gap, but metallic surface states, protected by the bulk gap. Recent work has shown, however, that certain gapless systems may also be topologically nontrivial, in a precise and experimentally observable way. In this talk I will review our work on a class of such systems, in which the nontrivial topological properties arise from the existence of nondegenerate point band-touching nodes (Weyl nodes) in their electronic structure. Weyl nodes generally exist in any three-dimensional material with a broken time-reversal or inversion symmetry. Their effect is particularly striking, however, when the nodes coincide with the Fermi energy and no other states at the Fermi energy exist. Such "Weyl semimetals" have vanishing bulk density of states, but have gapless metallic surface states with an open (unlike in a regular two-dimensional metal) Fermi surface ("Fermi arc"). I will discuss our proposal to realize Weyl semimetal state in a heterostructure, consisting of alternating layers of topological and ordinary insulator, doped with magnetic impurities. I will further show that, apart from Weyl semimetals, even such "ordinary" materials as common metallic ferromagnets, in fact also possess Weyl nodes in the electronic structure, leading to the appearance of chiral Fermi-arc surface states and the corresponding contribution to their intrinsic anomalous Hall conductivity.
Tuning magnetism and Chern bands in spin-orbit coupled double perovskites

Arun Paramekanti
University of Toronto

February 11, 2014

PIRSA:14020116

We show that double perovskites with 3d and 5d transition metal ions exhibit spin-orbit coupled magnetic excitations, finding good agreement with neutron scattering experiments in bulk powder samples. Motivated by experimental developments in the field of oxide heterostructures, we also study double perovskites films grown along the [111] direction. We show that spin-orbit coupling in such low dimensional systems can drive ferromagnetic order due to electronic correlations. This results in topological Chern bands, with symmetry-allowed trigonal deformations leading to quantum anomalous Hall states supporting a pair of chiral edge modes.
Fractional Quantum Hall Effect in a curved space

Pavel Wiegmann

February 11, 2014

PIRSA:14020112

We developed a general method to compute the correlation functions of FQH states on a curved space. The computation features the gravitational trace anomaly and reveals geometric properties of FQHE. Also we highlight a relation between the gravitational and electromagnetic response functions. The talk is based on the recent paper with T. Can and M. Laskin.
Geometry of topological matter: some examples

Duncan Haldane
Princeton University

February 12, 2014

PIRSA:14020117

I will look at two cases of the interplay of geometry (curvature) and topology:
(1) 3D Topological metals: how to understand their surface "Fermi arcs" in terms of their emergent conservation laws and the Streda formula for the non-quantized anomalous Hall effect.
(2) The Hall viscosity tensor in the FQHE as a local field, and its Gaussian-curvature response that allows local compression or expansion of the fluid to accommodate substrate inhomogeneity.
Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics

Dmitry Abanin

February 12, 2014

PIRSA:14020127

We demonstrate that the many-body localized phase is characterized by the existence of infinitely many local conservation laws. We argue that many-body eigenstates can be obtained from product states by a sequence of nearly local unitary transformation, and therefore have an area-law entanglement entropy, typical of ground states. Using this property, we construct the local integrals of motion in terms of projectors onto certain linear combinations of eigenstates [1]. The local integrals of motion can be viewed as effective quantum bits which have a conserved z-component that cannot decay. Thus, the dynamics is reduced to slow dephasing between distant effective bits. For initial product states, this leads to a characteristic slow power-law decay of local observables, which is measurable experimentally, as well as to logarithmic in time growth of entanglement entropy [2,3]. We support our findings by numerical simulations of random-field XXZ spin chains. Our work shows that the many-body localized phase is locally integrable, reveals a simple entanglement structure of eigenstates, and establishes the laws of dynamics in this phase.

[1] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. Lett. 111, 127201 (2013).
[2] Jens H. Bardarson, Frank Pollmann, and Joel E. Moore, Phys. Rev. Lett. 109, 017202 (2012).
[3] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. Lett. 110, 260601 (2013)
Geometrical dependence of information in 2d critical systems

Paul Fendley
University of Oxford

February 12, 2014

PIRSA:14020119

In both classical and quantum critical systems, universal contributions to the mutual information and Renyi entropy depend on geometry. I will first explain how in 2d classical critical systems on a rectangle, the mutual information depends on the central charge in a fashion making its numerical extraction easy, as in 1d quantum systems. I then describe analogous results for 2d quantum critical systems. Specifically, in special 2d quantum systems such as quantum dimer/Lifshitz models, the leading geometry-dependent term in the Renyi entropies can be computed exactly. In more common 2d quantum systems, numerical computations of a corner term hint toward the existence of a universal quantity providing a measure of the number of degrees of freedom analogous to the central charge.
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators.

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

February 12, 2014

PIRSA:14020120

A 3d electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface termination of an ETI supports an odd number of Dirac cones. In this talk, I will show that in the presence of strong interactions, an ETI surface can actually be gapped and symmetry preserving, at the cost of carrying an intrinsic two-dimensional topological order. I will argue that such a topologically ordered phase can be obtained from the surface superconductor by proliferating the flux 2hc/e vortex. The resulting topological order consists of two sectors: a Moore-Read sector, which supports non-Abelian charge e/4 anyons, and an Abelian anti-semion sector, which is electrically neutral. The time-reversal and particle number symmetries are realized in this surface phase in an "anomalous" way: one which is impossible in a strictly 2d system. If time permits, I will discuss related results on topologically ordered surface phases of 3d topological superconductors.
Quantum Tapestries

Matthew Fisher
University of California, Santa Barbara

February 12, 2014

PIRSA:14020121

Within each of nature's crystals is an exotic quantum world of electrons weaving to and fro. Each crystal has it's own unique tapestry, as varied as the crystals themselves. In some crystals, the electrons weave an orderly quilt. Within others, the electrons are seemingly entwined in an entangled web of quantum motion. In this talk, I will describe the ongoing efforts to disentangle even nature's most intricate quantum embroidery. Cutting-edge quantum many-body simulations together with recent ideas from quantum information theory, such as entanglement entropy, are enabling a coherent picture to emerge.

Title	Speaker(s)	Date	Talk Type	Info
Topological phases in graphene	Zlatko Papic	2014-02-10	Conference	View details
Aharonov-Bohm effect in symmetry protected states	Luiz Santos	2014-02-10	Conference	View details
Emergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice	Zheng-Cheng Gu	2014-02-10	Conference	View details
Specific heat and ac susceptibility measurements on the Spin Ice, Dy2Ti2O7	Jan Kycia	2014-02-11	Conference	View details
Topological response in gapless systems: from Weyl semimetals to metallic ferromagnets	Anton Burkov	2014-02-11	Conference	View details
Tuning magnetism and Chern bands in spin-orbit coupled double perovskites	Arun Paramekanti	2014-02-11	Conference	View details
Fractional Quantum Hall Effect in a curved space	Pavel Wiegmann	2014-02-11	Conference	View details
Geometry of topological matter: some examples	Duncan Haldane	2014-02-12	Conference	View details
Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics	Dmitry Abanin	2014-02-12	Conference	View details
Geometrical dependence of information in 2d critical systems	Paul Fendley	2014-02-12	Conference	View details
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators.	Max Metlitski	2014-02-12	Conference	View details
Quantum Tapestries	Matthew Fisher	2014-02-12	Conference	View details

Emergence in Complex Systems

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