Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session V03: Topological Spin LiquidsFocus
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Sponsoring Units: DCMP GMAG Room: BCEC 107B |
Thursday, March 7, 2019 2:30PM - 2:42PM |
V03.00001: Solvable 3D classical statistical models and a spin-fermion mapping Zhiyuan Wang, Kaden R A Hazzard In this talk, I will describe an exactly solvable classical statistical model on a 3D lattice. The model has two classical topological phases (one of which has been introduced previously [1]), and a finite-temperature phase transition between them. In contrast to prior 3D solvable statistical models [2], our system is much simpler, yet does not trivially reduce to a 2D model, and thus displays genuinely 3D correlations. Excitingly, this provides the first exactly solvable model in which to explore genuinely 3D critical phenomena; a caveat, however, is that the model Hamiltonian has imaginary terms. The construction and solution of this model are the first application of a new method that we introduce, developing ideas of [3], to map between a locally interacting fermionic Hamiltonian and a locally interacting spin Hamiltonian, in arbitrary dimension, in a simple way based on the use of algebraic isomorphisms. We expect that the spin-fermion mapping can be used not only for exact solutions, but for other applications such as numerical algorithms or perturbative calculations. |
Thursday, March 7, 2019 2:42PM - 2:54PM |
V03.00002: Higher Order Bosonic Topological Phases in Spin Models Oleg Dubinkin, Taylor Hughes Motivated by the recent discovery of the higher order topological phases in the fermionic systems we propose a natural extension of these phases to bosonic systems. We discuss two bosonic models for a second-order topological phase protected by a global Z2 x Z2 symmetry. One model is built from layers of an exactly solvable cluster model for a one-dimensional Z2 x Z2 topological phase. The other is built from more conventional spin-couplings (XY or Heisenberg) and repeats the structure of the quadrupole model. These models host gapped, but topologically protected, edges, as well as protected corner modes that fall into a projective representation of the symmetry. Using Jordan-Wigner transformations we show that our models are both related to a bilayer of free Majorana fermions that form a fermionic second-order topological phase. In fact, the XY model was shown to be in exact correspondence with the fermionic Quadrupole model. We also discuss possible extension to 3D bosonic models for 2nd and 3rd order topological phases. |
Thursday, March 7, 2019 2:54PM - 3:06PM |
V03.00003: The Cyclotron resonance as a smoking gun for U(1) spin liquids with gapless fermions Peng Rao, Inti Sodemann Certain U(1) spin liquids with gapless neutral fermions are expected to have the mind-boggling property that their optical conductivity vanishes as a power law of frequency. Thus, they are insulators to DC electric fields but without a "hard" optical gap, allowing them to absorb light at low frequencies. Additionally, they can also develop Landau levels in a magnetic field. In this work, we show that they can also have cyclotron resonance peaks in their optical spectrum analogous to metals, even though they are charge insulators. Interestingly, we have found that in contrast to metals, the principal Kohn harmonic of the cyclotron resonance is missing. The cyclotron resonance could therefore serve as a beautiful smoking gun test for the existence of these states which have been proposed in 2D organic materials and SmB6. |
Thursday, March 7, 2019 3:06PM - 3:18PM |
V03.00004: A Microscopic Definition of the F-symbol Kyle Kawagoe, Michael Levin The theory of anyons is a powerful tool for studying interacting topological phases of matter in two spatial dimensions. In this approach, topological phases are characterized by the properties of their anyonic excitations --- in particular, the statistical phases associated with braiding or fusing anyons. Some of these statistical phases, however, are missing a precise definition that would allow for their computation from a microscopic Hamiltonian. In this talk, we will address this issue by giving a microscopic definition of the “F-symbol” --- one of the most poorly understood pieces of data that characterize anyons. We will show that our definition is consistent with known values of the F-symbol and can easily be applied to new systems as well. |
Thursday, March 7, 2019 3:18PM - 3:30PM |
V03.00005: Symmetric gauge theories and Lieb-Schultz-Mattis-type constraints Xu Yang, Ying Ran It is known that certain symmetric gauge theories can only exist on the surface of a higher dimensional symmetry protected topological (SPT) state, in which case the symmetric gauge theory is anomalous. The anomaly class of such a gauge theory is represented by the bulk SPT index. Given an anomaly class, what kind of the symmetric gauge theories are allowed? Based on physical arguments and tensor-network constructions, we point out a sharp mathematical relationship between the symmetry properties of Abelian gauge theories and the anomaly class: the cup product. When the physical system hosts Lieb-Schultz-Mattis-type constraints, which is a specific type of anomaly class, our result sharply determines the physically allowed symmetric gauge theories via the preimage of the cup product. As applications, we algebraically compute the physically allowed skyrmion quantum numbers in various Neel states in 2+1D, and gauge charge/monopole projective representations in U(1) quantum spin liquids in 3+1D. We also compute the allowed Z2 gauge theories in several 2+1D quantum spin systems. |
Thursday, March 7, 2019 3:30PM - 3:42PM |
V03.00006: A model of symmetry enriched topological phases and its symmetry breaking gapped boundaries Bowen Shi, Yuanming Lu We present a model of symmetry enriched topological phases (SET) based on the toric code model, with symmetry group being the tensor product of translation and a Z2 onsite unitary symmetry. The symmetry does not permute anyon types and the model is in a nontrivial symmetry fractionalization class. We also discuss a gapped boundary with spontaneous symmetry breaking (SSB). This boundary condenses e anyon in the usual way, and the excitations at the boundary are domain walls. A domain containing an even number of effective spins could be created locally and a domain with an odd number of effective spins carry m charge. On a cylinder with an odd circumference, the Z2 symmetry permutes the minimal entangled states (MESs). A boundary with odd circumference could absorb an m by flipping all its effective spins. This leads to a correlation of symmetry breaking sectors at the boundary to the bulk MES sectors. |
Thursday, March 7, 2019 3:42PM - 3:54PM |
V03.00007: ABSTRACT WITHDRAWN
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Thursday, March 7, 2019 3:54PM - 4:06PM |
V03.00008: Thermal Transport Study of the Dimerized Quantum Magnet Strontium Copper Borate Colin Tinsman, Ziji Xiang, Lu Chen, Dmitri Mihaliov, Sara Haravifard, Lu Li Strontium Copper Borate (SrCu2(BO3)2, or SCBO) has a unique crystal structure in which pairs of copper atoms with spin-1/2 states hybridize to form spin-1 dimers, making it a realization of the Shastry Sutherland model. This compound has a singlet ground state at each dimer seperated by an energy gap from a triplet excitated state. It is predicted that this system should contain topologically-protected edge states consisting of itinerant triplets known as triplons, making SCBO a bosonic topological insulator. Since these triplons do not carry charge, thermal measurements are required to observe them. We report on the field-dependent thermal conductivity of this material as well as our progress in observing triplon states using the thermal Hall effect. |
Thursday, March 7, 2019 4:06PM - 4:18PM |
V03.00009: Entanglement Spectra of Stabilizer Codes: A Window into Fracton Order and Sub-System Symmetry Protected Topological States Albert Schmitz, Sheng-Jie Huang, Abhinav Prem We discuss the entanglement spectrum (ES) for stabilizer Hamiltonians with arbitrary weak local perturbations to contrast the entanglement features of gapped topological phases. In particular, we compare fracton order to both conventional topological order and sub-system symmetry-protected topological (SSPT) order. Our results show that non-local surface stabilizers (NLSS)—a set of symmetries of the Hamiltonian formed along the boundary of the entanglement cut—protect the universal non-local features of the ES. In conventional topological and fracton orders, some NLSS retain a form of topological invariance, whereas subsystem symmetric systems—fracton and SSPT phases—show a non-trivial geometric dependence corresponding to the sub-system symmetries. This demonstrates the interplay of geometry and topology in fracton phases as encoded in the ground states of the phase. We further show a version of the edge-entanglement correspondence in three dimensions. |
Thursday, March 7, 2019 4:18PM - 4:30PM |
V03.00010: Topological Transitions and the Spectral Function in the Kitaev-Ising Honeycomb Model Erik Aldape, Ruben Verresen, Ehud Altman
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Thursday, March 7, 2019 4:30PM - 4:42PM |
V03.00011: Classification of Symmetry Enriched Topological Phases Under Spatial Groups Interchanging Anyons Tianfu Fu, Andriy Nevidomskyy, Fiona Burnell Symmetry classification of 2d topologically ordered phases, such as topological spin liquids, has received much attention in the past. Previous works have focused on the trivial group action, where symmetries (spatial or internal) do not exchange the anyons. In this work, we extend classification to cases where the group action is nontrivial so that a subset of symmetry elements exchanges the anyon types. We formulate a general framework, based on the theory of group extensions, and apply it to the Z2 topological phases considering the 17 2d space groups under all possible nontrivial group actions. We demonstrate that the symmetry localization is no longer possible, meaning that two-particle symmetry operations cannot be written as a direct product of the one-particle actions. Moreover, because the anyons are exchanged by the symmetry group, it is no longer possible to discuss symmetry fractionalization that would assign a symmetry class for each anyon independently, and instead projective representations of different anyon types become intertwined. We show that the symmetry classification can nevertheless be formulated in a mathematical rigorous way, and prove its application to the Wen plaquette model on a square lattice as a special case. |
Thursday, March 7, 2019 4:42PM - 4:54PM |
V03.00012: Foliated Quantum Field Theory of Fracton Order and String-Membrane-Net Condensation Kevin Slagle, David Aasen, Dominic Williamson Foliated fracton order is a new kind of phase of matter which is similar to topological order, but where a layered structure, referred to as a foliation, plays an essential role (in addition to topology) and determines the mobility restrictions of the topological excitations characteristic of fracton phases. I will introduce a new kind of field theory to describe these phases: a foliated field theory. I will also introduce a new string-membrane-net condensation picture of these phases, which is analogous to the string-net condensation picture of topological order. |
Thursday, March 7, 2019 4:54PM - 5:06PM |
V03.00013: Thermal Hall effect in the quantum spin liquid candidate α-RuCl3 Etienne Lefrancois, Gael Grissonnanche, Paula J Kelley, Christian Balz, Jiaqiang Yan, David George Mandrus, Stephen Nagler, Louis Taillefer Kasahara et al. have reported the observation of a quantized thermal Hall conductivity κxy in the Kitaev spin-liquid candidate α-RuCl3 at low temperature, when antiferromagnetic order is suppressed with an in-plane magnetic field [1]. The reported magnitude of κxy / T is consistent with the quantized value expected from topologically protected chiral edge currents of charge-neutral Majorana fermions [2]. If confirmed, this is a major advance in the physics of quantum spin liquids. |
Thursday, March 7, 2019 5:06PM - 5:18PM |
V03.00014: Electrical probes of the non-Abelian spin liquid phase in α-RuCl3 David Aasen, Roger Mong, Benjamin Matthew Hunt, David George Mandrus, Jason Alicea Recent thermal-transport experiments indicate that the Kitaev material α-RuCl3 realizes a non-Abelian spin liquid with Ising topological order over a range of magnetic fields. We propose a series of measurements for electrically detecting the hallmark chiral Majorana edge states and bulk anyons in the spin-liquid phase -- despite the fact that α-RuCl3 is a good Mott insulator. In particular, we introduce circuits that exploit interfaces between electronic systems and α-RuCl3 to convert physical fermions into emergent fermions, thus enabling analogues of transport probes of non-Abelian-anyon physics in topological superconductors. We further propose detection of individual bulk neutral fermions via a spin counterpart of charge sensing. Our results illuminate a partial pathway towards using Kitaev materials for topological quantum computation. |
Thursday, March 7, 2019 5:18PM - 5:30PM |
V03.00015: Thermal Hall effect in square-lattice spin liquids Rhine Samajdar, Shubhayu Chatterjee, Mathias Scheurer, Subir Sachdev The extension of the notion of a topology-driven Hall effect to charge-neutral excitations has been an exciting theoretical development. Motivated by recent experimental observations in high-Tc cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from the deconfined neutral gapped spinons in the insulating state. More specifically, we examine different Schwinger-boson mean-field ansätze for the Heisenberg antiferromagnet on the square lattice, allowing for both Dzyaloshinskii-Moriya interactions and additional terms that break time-reversal and reflection symmetries but preserve their product. We show that the bosonic bands acquire nontrivial Chern numbers and evaluate the thermal Hall coefficient. On top of a significantly enhanced conductivity, which should yield a sizable experimental signal, we also observe an anomalous contribution. |
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