Higher-form gauge symmetries in multipole topological phases

Dubinkin, Oleg; Rasmussen, Alex; Hughes, Taylor L.

doi:10.1016/j.aop.2020.168297

Cited by 27 publications

(41 citation statements)

References 49 publications

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“…We will denote the gauge fields by A andÂ, respectively. Certain aspects of the gauge theory of A have been discussed in [20,21,24,[30][31][32] (see [22,23,25,27,28,[33][34][35][36][37][38][39][40][41][42][43][44] for related tensor gauge theories). The gauge theory ofÂ is related to gauge theories discussed in [20].…”

Section: Preview Of [1 2]mentioning

confidence: 99%

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Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

2021

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We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

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Section: Preview Of [1 2]mentioning

confidence: 99%

“…Motivated by earlier papers about related models, this gauge theory was studied in [22,23,31,33]. The Lorentzian Lagrangian of the pure tensor gauge theory is…”

Section: Lagrangianmentioning

confidence: 99%

Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

2021

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“…Let us focus on a subset of the symmetry operators: the N tensor symmetry operator extended along the z direction (3.14)Ŵ z (x 0 , y 0 ) (4. 31) and the N dipole symmetry strip operators on the x y-plane (2.12)…”

Section: Ground State Degeneracy From Global Symmetriesmentioning

confidence: 99%

“…it is a U(1) (2, 3 ) tensor symmetry. Some aspects of the A-theory had been discussed in [10][11][12][13][14][15] (see [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] for related tensor gauge theories). And some aspects of theÂ-gauge theory had been discussed in [11].…”

Section: Introductionmentioning

confidence: 99%

Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

2021

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Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the low-energy physics of the X-cube model. A key aspect of our constructions is the use of discontinuous fields in the continuum field theory. Spacetime is continuous, but the fields are not.

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“…For similar ideas, see Refs. [45,46]. The "missing" elasticity tetrad fields enter in new crystalline topological terms and contain a mixture of the electromagnetic A μ and elastic E a μ gauge fields [44], as we discuss next.…”

Section: A Elasticity Tetradsmentioning

confidence: 99%

Topological polarization, dual invariants, and surface flat bands in crystalline insulators

2021

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We describe a crystalline topological insulator (TI) phase of matter that exhibits spontaneous polarization in arbitrary dimensions. The bulk polarization response is constructed by coupling the system to geometric deformations of the underlying crystalline order, represented by local lattice vectors-the elasticity tetrads. This polarization results from the presence of (approximately) flat bands on the surface of such TIs. These flat bands are a consequence of the bulk-boundary correspondence of polarized topological media, and contrary to related nodal line semimetal phases also containing surface flat bands, they span the entire surface Brillouin zone. We also present an example Hamiltonian exhibiting a Lifshitz transition from the nodal line phase to the TI phase with polarization. In addition, we discuss a general classification of three-dimensional (3D) crystalline TI phases and invariants in terms of the elasticity tetrads. The phase with polarization naturally arises from this classification as a dual to the previously better-known 3D TI phase exhibiting quantum (spin) Hall effect. Besides polarization, another implication of the large surface flat band is the susceptibility to interaction effects such as superconductivity: The mean-field critical temperature is proportional to the size of the flat bands, and this type of system may hence exhibit superconductivity with a very high critical temperature.

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Higher-form gauge symmetries in multipole topological phases

Cited by 27 publications

References 49 publications

Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

Topological polarization, dual invariants, and surface flat bands in crystalline insulators

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