Topological Order and Symmetry Anomaly on the Surface of Topological Crystalline Insulators

Hong, Sungjoon; Fu, Liang

doi:10.48550/arxiv.1707.02594

Cited by 13 publications

(14 citation statements)

References 61 publications

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“…Translation by a wire then interchanges even and odd links, thus acting as an anyon-relabelling transformation. A similar mechanism has been featured in the work by Hong and Fu [50], where a fermionic Z 4 topological order is realized on the surface of topological crystalline insulators. Consequently, a dislocation in our wire model, which corresponds to a sudden termination of a wire inside the bulk, acts as a twofold twist-defect that interchanges e and m anyons [47].…”

supporting

confidence: 60%

Non-diagonal anisotropic quantum Hall states

Tam,

Kane

2020

Preprint

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We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors ν = p/2q for bosonic systems and ν = p/(p + 2q) for fermionic systems, with p and q being two coprime integers. Non-diagonal quantum Hall states are constructed in a coupled wire model, which shows an intimate relation to the non-diagonal conformal field theory and has a constrained pattern of motion for bulk quasiparticles, featuring a non-trivial interplay between charge symmetry and translation symmetry. The non-diagonal state is established as a distinctive symmetry-enriched topological order. Aside from the usual U (1) charge sector, there is an additional symmetry-enriched neutral sector described by the quantum double model D(Zp), which relies on the presence of both the U (1) charge symmetry and the Z translation symmetry of the wire model. Translation symmetry distinguishes non-diagonal states from Laughlin states, in a way similar to how it distinguishes weak topological insulators from trivial band insulators. Moreover, the translation symmetry in non-diagonal states can be associated to the e ↔ m anyonic symmetry in D(Zp), implying the role of dislocations as two-fold twist-defects. The boundary theory of non-diagonal states is derived microscopically. For the edge perpendicular to the direction of wires, the effective Hamiltonian has two components: a chiral Luttinger liquid and a generalized p-state clock model. Importantly, translation symmetry in the bulk is realized as self-duality on the edge. The symmetric edge is thus either gapless or gapped with spontaneously broken symmetry. For p = 2, 3, the respective electron tunneling exponents are predicted for experimental probes. CONTENTS A. Constructing the fermionic states 22References 23

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supporting

confidence: 60%

Non-diagonal anisotropic quantum Hall states

Tam,

Kane

2020

Preprint

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“…The theory of interacting SPT phases protected by internal symmetries, studied via gauging procedures and other techniques, is by now well-developed. On the other hand, interacting SPT phases protected by crystal symmetries have only been studied relatively recently [115][116][117][118][119][120][121] , and the set of available tools has been more limited. Nevertheless, we expect that the gauging procedure applied to simpler SPT phases can be adapted to the case of crystal symmetries by the identification of a corresponding gauge "flux."…”

Section: Connection To Topological Crystalline Insulatorsmentioning

confidence: 99%

Crystal-to-fracton tensor gauge theory dualities

2019

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We demonstrate several explicit duality mappings between elasticity of two-dimensional crystals and fracton tensor gauge theories, expanding on recent works by two of the present authors. We begin by dualizing the quantum elasticity theory of an ordinary commensurate crystal, which maps directly onto a fracton tensor gauge theory, in a natural tensor analogue of the conventional particlevortex duality transformation of a superfluid. The transverse and longitudinal phonons of a crystal map onto the two gapless gauge modes of the tensor gauge theory, while the topological lattice defects map onto the gauge charges, with disclinations corresponding to isolated fractons and dislocations corresponding to dipoles of fractons. We use the classical limit of this duality to make new predictions for the finite-temperature phase diagram of fracton models, and provide a simpler derivation of the Halperin-Nelson-Young theory of thermal melting of two-dimensional solids. We extend this duality to incorporate bosonic statistics, which is necessary for a description of the quantum melting transitions. We thereby derive a hybrid vector-tensor gauge theory which describes a supersolid phase, hosting both crystalline and superfluid orders. The structure of this gauge theory puts constraints on the quantum phase diagram of bosons, and also leads to the concept of symmetry enriched fracton order. We formulate the extension of these dualities to systems breaking timereversal symmetry. We also discuss the broader implications of these dualities, such as a possible connection between fracton phases and the study of interacting topological crystalline insulators.

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“…A decade of intense effort has resulted in a thorough classification and characterization of symmetry protected topological phases of fermionic and bosonic systems [1][2][3][4]. In a recent step forward, the concept of symmetry protection has been extended to include spatial symmetries [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In addition to protected gapless boundary modes, some topological crystalline phases admit gapped edges or surfaces separated by gapless corners or hinges, exemplifying a much richer bulk-boundary correspondence.…”

Section: Introductionmentioning

confidence: 99%

Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases

You,

Bibo,

Pollmann

2020

Preprint

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We discuss how strongly interacting higher-order symmetry protected topological (HOSPT) phases can be characterized from the entanglement perspective: First, we introduce a topological many-body invariant which reveals the non-commutative algebra between flux operator and Cn rotations. We argue that this invariant denotes the angular momentum carried by the instanton which is closely related to the discrete Wen-Zee response and the fractional corner charge. Second, we define a new entanglement property, dubbed 'higher-order entanglement', to scrutinize and differentiate various higher-order topological phases from a hierarchical sequence of the entanglement structure. We support our claims by numerically studying a super-lattice Bose-Hubbard model that exhibits different HOSPT phases.

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Topological Order and Symmetry Anomaly on the Surface of Topological Crystalline Insulators

Cited by 13 publications

References 61 publications

Non-diagonal anisotropic quantum Hall states

Non-diagonal anisotropic quantum Hall states

Crystal-to-fracton tensor gauge theory dualities

Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases

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