Bulletin of the American Physical Society
APS March Meeting 2021
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 lowlying levels of a (2+1)D chiral topological state's entanglement spectrum (ES), numerically computed across a finite realspace 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 higherorder 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) ChernSimons theory at levels one and two. We find that splittings in the lowlying ES are well characterized by a number of higherorder 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 qdeformed bilinearbiquadratic spin chain and the associated quantum group invariant AKLT model Thomas Quella We argue that the qdeformed spin1 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 spin1/2 boundary spins, nontrivial string order and  when using an appropriate definition  a twofold degeneracy in the entanglement spectrum. Numerical computations using iDMRG show that these features also persist in parts of the phase diagram of the qdeformed bilinearbiquadratic 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 nonAbelian models YiTing Tu, PoYao Chang We summarize several different gaugetheoryrelated formulations of quantum stabilizer codes on a lattice. Examples include the toric code and the Xcube model. The latter carries fractonic excitations. We compare and contrast these formulations, and investigate their generalizations to nonAbelian gauge theories. In particular, we construct the nonAbelian anyon model from gauging the SWAP symmetry of doublelayer Z_{2} gauge theory with matter and compare it with the D_{4} 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 timereversal symmetric unitary operators in one and two spatial dimensions, by gauging the socalled KuboMartinSchwinger (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 LiebShultzMattis (LSM) theorems constrain the lowenergy 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 LSMtype anomalies. In particular, we rigorously constrain the allowed values of the central charge for certain CFTs with an LSMtype anomaly that can describe fixed points of symmetryenforced gapless phases. 
Friday, March 19, 2021 12:30PM  12:42PM Live 
Y46.00006: Protection of paritytime symmetry in topological manybody systems Henry Shackleton, Mathias Scheurer In the study of PTsymmetric quantum systems with nonHermitian 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 groundstate 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 manybody 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 nonHermitian 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 coupledwire 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 D_{k} 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} / Z_{2}, SO(2n)_{1} / Z_{k}, SU(n)_{1 }/ Z_{2} and SO(2n)_{1 }/ D_{k}, 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 GarreRubio, 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 twodimensional subsystem symmetryprotected topological orders. This decoration causes the looplike 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 shortrange entangled model which has symmetryprotected 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 Twodimensional 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 Z_{2} 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 twoparticle symmetry operations cannot be written as a direct product of the oneparticle 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 2group SPT phases in (3+1)D YuAn Chen, Tyler Ellison, Nathanan Tantivasadakarn Symmetryprotected topological (SPT) phases of matter are described by shortrange entangled states. For each bosonic SPT phase described by the group cohomology, there is a fixedpoint 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 2group symmetry to supercohomology phases. A short overview is that gauging the 1form 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 1form 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 
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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