Dual gauge field theory of quantum liquid crystals in three dimensions

Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai; Zaanen, Jan

doi:10.1103/physrevb.96.165115

Cited by 48 publications

(58 citation statements)

References 95 publications

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“…the dimension [L] −1 . This is consistent with the fact, that in the presence of dislocations, the three vielbein fields become the torsion gauge fields of the local U(1) × U(1) × U(1) group of broken translation symmetry of crystals modulo the periodicity of the Bravais lattice 29 . The field strengths of these gauge fields correspond to the torsion, expressed via tetrads according to Eq.…”

Section: Discussionsupporting

confidence: 86%

Tetrads in Solids: from Elasticity Theory to Topological Quantum Hall Systems and Weyl Fermions

Nissinen

Volovik

2018

J. Exp. Theor. Phys.

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Theory of elasticity in topological insulators has many common features with relativistic quantum fields interacting with gravitational field in the tetrad form. Here we discuss several issues in the effective topological (pseudo)electromagnetic response in three-dimensional weak crystalline topological insulators with no time-reversal symmetry that feature elasticity tetrads, including a mixed "axial-gravitational" anomaly. This response has some resemblance to "quasitopological" terms proposed for massless Weyl quasiparticles with separate, emergent fermion tetrads. As an example, we discuss the chiral/axial anomaly in superfluid 3 He-A. We demonstrate the principal difference between the elasticity tetrads and the Weyl fermion tetrads in the construction of the topological terms in the action. In particular, the topological action expressed in terms of the elasticity tetrads, cannot be expressed in terms of the Weyl fermion tetrads since in this case the gauge invariance is lost.PACS numbers:

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Section: Discussionsupporting

confidence: 86%

Tetrads in Solids: from Elasticity Theory to Topological Quantum Hall Systems and Weyl Fermions

Nissinen

Volovik

2018

J. Exp. Theor. Phys.

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“…Since condensed matter systems usually break translational invariance in nature, we have considered holographic duals of such systems with homogeneity and isotropy properties using the language of dRGT massive gravity with a singular, degenerate reference metric. We obtained TBH solutions that are free from pathological behavior and dual to matter with broken translational symmetry property; so, in principle, they can be dual to liquid crystals [33,45,46]. These TBHs yield up to n = (d − 4) critical points in d dimensions.…”

Section: Closing Remarksmentioning

confidence: 99%

Range of novel black hole phase transitions via massive gravity: Triple points and N -fold reentrant phase transitions

2020

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Massive gravities in anti-de Sitter spacetime can be viewed as effective dual field theories of different phases of condensed matter systems with broken translational symmetry such as solids, (perfect) fluids, and liquid crystals. Motivated by this fact, we explore the black hole chemistry (BHC) of these theories and find a new range of novel phase transitions close to realistic ones in ordinary physical systems. We find that the equation of state of topological black holes (TBHs) at their inflection point(s) in d-dimensional spacetime reduces to a polynomial equation of degree (d−4), which yields up to n = (d−4) critical points. As a result, for (neutral) TBHs, we observe triple-point phenomena with the associated first-order phase transitions (in d ≥ 7), and a new phenomenon we call an N-fold reentrant phase transition, in which several (N) regions of thermodynamic phase space exhibit distinct reentrant phase transitions, with associated virtual triple points and zerothorder phase transitions (in d ≥ 8), as well as Van der Waals transitions (in d ≥ 5) and reentrant (in d ≥ 6) behavior. We conclude that BHC in higher-dimensional massive gravity is very likely to offer further new surprises.

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“…We note the existence of several related gauge theory dualities concerning elasticity theory. [30][31][32][33] While fracton-elasticity duality 4 provides a useful description of a Mott-insulating "commensurate" crystal (with gapped vacancy/interstitial defects) and offers an insightful embodiment of fracton phenomena, it is not immediately clear how such a formulation can capture a quantum melting transition to non-crystalline phases of the underlying atoms. Specifically, the tensor-only gauge theory 4 is incomplete as it does not incorporate the quantum statistics of the constituent particles, which is essential in a fluid state.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-Enriched Fracton Phases from Supersolid Duality

Pretko

Radzihovsky

2018

Phys. Rev. Lett.

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Motivated by the recently established duality between elasticity of crystals and a fracton tensor gauge theory, we combine it with boson-vortex duality, to explicitly account for bosonic statistics of the underlying atoms. We thereby derive a hybrid vector-tensor gauge dual of a supersolid, which features both crystalline and superfluid order. The gauge dual describes a fracton state of matter with full dipole mobility endowed by the superfluid order, as governed by "mutual" axion electrodynamics between the fracton and vortex sectors of the theory, with an associated generalized Witten effect. Vortex condensation restores U (1) symmetry, confines dipoles to be subdimensional (recovering the dislocation glide constraint of a commensurate quantum crystal), and drives a phase transition between two distinct fracton phases. Meanwhile, condensation of elementary fracton dipoles and charges, respectively, provide a gauge dual description of the super-hexatic and ordinary superfluid. Consistent with conventional wisdom, in the absence of crystalline order, U (1)-symmetric phases are prohibited at zero temperature via a mechanism akin to deconfined quantum criticality. arXiv:1808.05616v2 [cond-mat.str-el]

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Dual gauge field theory of quantum liquid crystals in three dimensions

Cited by 48 publications

References 95 publications

Tetrads in Solids: from Elasticity Theory to Topological Quantum Hall Systems and Weyl Fermions

Tetrads in Solids: from Elasticity Theory to Topological Quantum Hall Systems and Weyl Fermions

Range of novel black hole phase transitions via massive gravity: Triple points and N -fold reentrant phase transitions

Symmetry-Enriched Fracton Phases from Supersolid Duality

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