Bulk characterization of topological crystalline insulators: Stability under interactions and relations to symmetry enriched 
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(1) quantum spin liquids

Zou, Liujun

doi:10.1103/physrevb.97.045130

Cited by 27 publications

(28 citation statements)

References 64 publications

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“…We expect that a more detailed understanding of fracton phases thus obtained by gauging crystal symmetries may prove useful for classifying interacting TCIs, a quest that is still being actively pursued. [70][71][72][73][74][75][76] We leave the details of implementing this program as a task for the future.…”

Section: (11)mentioning

confidence: 99%

Fracton-Elasticity Duality

2018

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Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.

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Section: (11)mentioning

confidence: 99%

Fracton-Elasticity Duality

2018

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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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“…Now we consider a U(1) gauge theory realized in a microscopic model with a global symmetry group G. We will analyze how global symmetry transformations are realized in the low-energy theory. For clarity, let us assume that G is internal, and we expect the results for spatial symmetries will be similar [24,25]. We will also consider the case where G includes lattice translation symmetry in some occasions.…”

Section: Symmetry Fractionalization and Anomalies In U(1) Gauge mentioning

confidence: 99%

Fractionalization and anomalies in symmetry-enriched U(1) gauge theories

Ning

Zou

Cheng

2020

Phys. Rev. Research

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We classify symmetry fractionalization and anomalies in a (3+1)d U(1) gauge theory enriched by a global symmetry group G. We find that, in general, a symmetry-enrichment pattern is specified by four pieces of data: ρ, a map from G to the duality symmetry group of this U(1) gauge theory which physically encodes how the symmetry permutes the fractional excitations, ν ∈ H 2 ρ [G, U T (1)], the symmetry actions on the electric charge, p ∈ H 1 [G, Z T ], indication of certain domain wall decoration with bosonic integer quantum Hall (BIQH) states, and a torsor n over H 3 ρ [G, Z], the symmetry actions on the magnetic monopole. However, certain choices of (ρ, ν, p, n) are not physically realizable, i.e., they are anomalous. We find that there are two levels of anomalies. The first level of anomalies obstruct the fractional excitations being deconfined, thus are referred to as the deconfinement anomaly. States with these anomalies can be realized on the boundary of a (4+1)d long-range entangled state. If a state does not suffer from a deconfinement anomaly, there can still be the second level of anomaly, the more familiar 't Hooft anomaly, which forbids certain types of symmetry fractionalization patterns to be implemented in an on-site fashion. States with these anomalies can be realized on the boundary of a (4+1)d short-range entangled state. We apply these results to some interesting physical examples.

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Bulk characterization of topological crystalline insulators: Stability under interactions and relations to symmetry enriched U (1) quantum spin liquids

Cited by 27 publications

References 64 publications

Fracton-Elasticity Duality

Fracton-Elasticity Duality

Crystal-to-fracton tensor gauge theory dualities

Fractionalization and anomalies in symmetry-enriched U(1) gauge theories

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