Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session Y46: Symmetries in Topological PhasesLive
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Sponsoring Units: DCMP Chair: Meng Cheng |
Friday, March 19, 2021 11:30AM - 11:42AM Live |
Y46.00001: Understanding the Chiral Topological Behavior of Certain PEPS Models Through Detection of Conserved Quantities from the Conformal Boundary State Description of the Real Space Entanglement Spectrum Mark Arildsen, Andreas W Ludwig Degeneracies in momentum of low-lying levels of a (2+1)D chiral topological state's entanglement spectrum (ES), numerically computed across a finite real-space cut, serve as a fingerprint of the topological nature of the bulk state. Using the conformal boundary state description, we examined the splittings of these degeneracies in systems with global SU(2) symmetry. The splittings arise from higher-order conservation laws of the conformal field theory (CFT) in the sense of a generalized Gibbs ensemble (GGE), strongly limited in number by global SU(2) symmetry. The ability to explain the splittings solely in the context of CFT via a GGE serves as a finer diagnostic (than the degeneracies alone) of the chiral topological behavior of the bulk. The capability of interacting PEPS tensor networks to describe chiral topological states is not understood. We analyzed earlier PEPS numerical studies with ES degeneracies characteristic of SU(2) Chern-Simons theory at levels one and two. We find that splittings in the low-lying ES are well characterized by a number of higher-order conservation laws. Thus, at the considered system sizes, the PEPS states appear chiral also under our more sensitive diagnostic. Notably, for level two, fermionic conservation laws of fractional spin are required. |
Friday, March 19, 2021 11:42AM - 11:54AM Live |
Y46.00002: Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain and the associated quantum group invariant AKLT model Thomas Quella We argue that the q-deformed spin-1 AKLT Hamiltonian should be regarded as a representative of a symmetry protected topological phase. Even though it fails to exhibit any of the standard symmetries known to protect the Haldane phase it still displays all characteristics of this phase: Fractionalized spin-1/2 boundary spins, non-trivial string order and - when using an appropriate definition - a two-fold degeneracy in the entanglement spectrum. Numerical computations using iDMRG show that these features also persist in parts of the phase diagram of the q-deformed bilinear-biquadratic spin chain whose structure is analyzed in detail. |
Friday, March 19, 2021 11:54AM - 12:06PM Live |
Y46.00003: Gauge Theories and Stabilizer Codes: From Abelian to non-Abelian models Yi-Ting Tu, Po-Yao Chang We summarize several different gauge-theory-related formulations of quantum stabilizer codes on a lattice. Examples include the toric code and the X-cube model. The latter carries fractonic excitations. We compare and contrast these formulations, and investigate their generalizations to non-Abelian gauge theories. In particular, we construct the non-Abelian anyon model from gauging the SWAP symmetry of double-layer Z2 gauge theory with matter and compare it with the D4 quantum double model. |
Friday, March 19, 2021 12:06PM - 12:18PM Live |
Y46.00004: Gauging anomalous unitary operators Yuhan Liu, Hassan Shapourian, Paolo Glorioso, Shinsei Ryu Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize unitary operators at their boundaries which are obstructed. In this paper, we discuss the characterization of such obstruction by using quantum anomalies. As a particular example, we discuss time-reversal symmetric unitary operators in one and two spatial dimensions, by gauging the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as C and CP, for unitary operators in odd spatial dimensions that can be realized at boundaries of topological Floquet systems in even spatial dimensions. |
Friday, March 19, 2021 12:18PM - 12:30PM Live |
Y46.00005: Mixed anomalies and the modular bootstrap Ryan Lanzetta, Lukasz Fidkowski Lieb-Shultz-Mattis (LSM) theorems constrain the low-energy physics of translationally invariant 1D lattice models with projective symmetry representations in each unit cell by preventing them from being trivially gapped. This leaves spontaneous symmetry breaking or gaplessness as the only possibilities. Furthermore, in the low energy effective field theory of such models there is a mixed ’t Hooft anomaly between the translation symmetry and the internal symmetry. We use the modular bootstrap to put quantitative bounds on aspects of (1+1)D conformal field theories (CFTs) that saturate these LSM-type anomalies. In particular, we rigorously constrain the allowed values of the central charge for certain CFTs with an LSM-type anomaly that can describe fixed points of symmetry-enforced gapless phases. |
Friday, March 19, 2021 12:30PM - 12:42PM Live |
Y46.00006: Protection of parity-time symmetry in topological many-body systems Henry Shackleton, Mathias Scheurer In the study of PT-symmetric quantum systems with non-Hermitian perturbations, one of the most important questions is whether eigenvalues stay real or whether PT symmetry is spontaneously broken when eigenvalues meet. A particularly interesting set of eigenstates is provided by the degenerate ground-state subspace of systems with topological order. We present simple criteria that guarantee the protection of PT symmetry and, thus, the reality of the eigenvalues in topological many-body systems. We formulate these criteria in both geometric and algebraic form and demonstrate them using the toric code and several different fracton models as examples. Our analysis reveals that PT symmetry is robust against a remarkably large class of non-Hermitian perturbations in these models; this is particularly striking in the case of fracton models due to the exponentially large number of degenerate states. |
Friday, March 19, 2021 12:42PM - 12:54PM Live |
Y46.00007: Climbing the ladder of topological bosonic orbifold phases in the orthogonal family: from gauging dihedral symmetry to metaplectic anyons and more Jeffrey Teo, Yichen Hu We present a coupled-wire model of a family of bosonic orbifold topological phases in two spatial dimensions using strongly interacting electrons with a charge 4e superconducting pairing. A topological phase M can carry a global discrete symmetry G. We focus on the bosonic SO(2n)1 family that exhibits a dihedral Dk symmetry. The symmetry may become local when the system undergoes a phase transition that allows gauge fluxes and charges to emerge. These new phases M / G, referred to as twist liquids, host boundary edge modes that can be effectively described by an orbifold conformal field theory. We explicitly demonstrate these in the bosonic orbifold series of U(1)l / Z2, SO(2n)1 / Zk, SU(n)1 / Z2 and SO(2n)1 / Dk, and present their quasiparticle excitations. |
Friday, March 19, 2021 12:54PM - 1:06PM Live |
Y46.00008: Subsystem Symmetry Enriched Topological Order in Three Dimensions David Stephen, José Garre-Rubio, Arpit Dua, Dominic J Williamson We construct a model of three dimensional (3D) topological order enriched by planar subsystem symmetries by decorating the 3D toric code with two-dimensional subsystem symmetry-protected topological orders. This decoration causes the loop-like excitations of the 3D toric code to fractionalize under the planar subsystem symmetries, resulting in an extensive degeneracy of the excitation and also an increased value of the topological entanglement entropy for certain bipartitions. Our model can be obtained by gauging the global symmetry of a short-range entangled model which has symmetry-protected topological order coming from an interplay of global and subsystem symmetries. We further study this interplay by gauging various subgroups of the symmetry, resulting in a network of models, including models with fracton topological order, which showcases more of the possible types of subsystem symmetry enrichment that can occur in 3D. |
Friday, March 19, 2021 1:06PM - 1:18PM Live |
Y46.00009: Symmetry Classfication of Two-dimensional Topologically Ordered Phases Under Exchange of 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. |
Friday, March 19, 2021 1:18PM - 1:30PM Live |
Y46.00010: Supercohomology symmetry protected topological (SPT) phases and bosonic 2-group SPT phases in (3+1)D Yu-An Chen, Tyler Ellison, Nathanan Tantivasadakarn Symmetry-protected topological (SPT) phases of matter are described by short-range entangled states. For each bosonic SPT phase described by the group cohomology, there is a fixed-point state that can be prepared by a finite depth quantum circuit (FDQC) built from the corresponding cohomology data. In this talk, a generalization for (3+1)D intrinsically interacting fermionic SPT phases, known as the supercohomology phases, will be introduced. The derivation of the FDQC utilizes a series of exact lattice dualities that relate bosonic SPT phases with a certain 2-group symmetry to supercohomology phases. A short overview is that gauging the 1-form symmetry of a bosonic model gives a Z2 lattice gauge theory, and bosonizing a fermionic model also gives a Z2 lattice gauge theory. These Z2 lattice gauge theories can match, and this constructs a duality between certain bosonic and fermionic models. The concepts of "gauging 1-form symmetry" and "bosonization (gauging fermion parity)" will be clearly explained. A primary result of this approach is that the “symmetry fractionalization” on fermion parity flux loops is immediate, which is the characteristic of supercohomology phases. |
Friday, March 19, 2021 1:30PM - 1:42PM On Demand |
Y46.00011: Entanglement bootstrap approach for gapped domain walls Bowen Shi, Isaac Kim We develop a theory of gapped domain wall between topologically ordered systems in two spatial dimensions. We find a new type of superselection sector -- referred to as the parton sector -- that subdivides the known superselection sectors localized on gapped domain walls. Moreover, we introduce and study the properties of composite superselection sectors that are made out of the parton sectors. We explain a systematic method to define these sectors, their fusion spaces, and their fusion rules, by deriving nontrivial identities relating their quantum dimensions and fusion multiplicities. We propose a set of axioms regarding the ground state entanglement entropy of systems that can host gapped domain walls, generalizing the bulk axioms proposed in. As an application, we define an analog of topological entanglement entropy for gapped domain walls and derive its exact expression. |
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