Two-dimensional melting via sine-Gordon duality

Zhai, Zhengzheng; Radzihovsky, Leo

doi:10.1103/physrevb.100.094105

Cited by 27 publications

(19 citation statements)

References 25 publications

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“…In turn, the duality allows the fracton formalism to shed additional light on the phase diagram of two-dimensional crystals. For example, the duality has been used to provide a simplified derivation of the Halperin-Nelson-Young theory of two-dimensional melting [44]. It has also been proposed that the duality may aid in the classification of interacting topological crystalline insulators [9,46].…”

Section: A Fracton-elasticity Dualitymentioning

confidence: 99%

“…This connection is made precise via a duality transformation, often referred to as "fracton-elasticity duality," which maps the elasticity theory of crystals onto a symmetric tensor gauge theory [9]. We discuss this duality in detail in Section V, along with its various generalizations [41][42][43][44][45][46][47]. For example, the duality can be extended to three-dimensional elasticity theory, giving rise to the concept of fractonic lines, i.e line-like excitations without the ability to move [41].…”

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confidence: 99%

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Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

343

269

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Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual phenomenology, such as gravitational physics and localization.The past several years have seen a surge of interest in these exotic particles, which have come to the forefront of modern condensed matter theory. In this review, we provide a broad treatment of fractons, ranging from pedagogical introductory material to discussions of recent advances in the field. We begin by demonstrating how the fracton phenomenon naturally arises as a consequence of higher moment conservation laws, often accompanied by the emergence of tensor gauge theories.We then provide a survey of fracton phases in spin models, along with the various tools used to characterize them, such as the foliation framework. We discuss in detail the manifestation of fracton physics in elasticity theory, as well as the connections of fractons with localization and gravitation.Finally, we provide an overview of some recently proposed platforms for fracton physics, such as Majorana islands and hole-doped antiferromagnets. We conclude with some open questions and an outlook on the field.

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Section: A Fracton-elasticity Dualitymentioning

confidence: 99%

mentioning

confidence: 99%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

343

269

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“…This shows that as long as g b is small, g s is strongly irrelevant with scaling dimension −2. 99 To study this crystal to hexatic fluid melting transition, we can entirely neglect disclinations, which remain bound across the transition. This allows us to simply drop the disclination piece of the vector sine-Gordon model, i.e.…”

Section: Renormalization Group Analysismentioning

confidence: 99%

Crystal-to-fracton tensor gauge theory dualities

2019

Self Cite

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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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“…The relationship between fracton phases of matter and elasticity has been noticed by several authors [36][37][38][39][40][41][42]. While formal details are different among these works, the essential observation is quite simple.…”

mentioning

confidence: 97%

On duality between Cosserat elasticity and fractons

Gromov

Surówka

2020

SciPost Phys.

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We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a vector-valued one-form gauge field and an ordinary U (1) gauge field. We discuss the degrees of freedom in the corresponding gauge theories, the defect matter and coupling to the curved space.

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Two-dimensional melting via sine-Gordon duality

Cited by 27 publications

References 25 publications

Fracton phases of matter

Fracton phases of matter

Crystal-to-fracton tensor gauge theory dualities

On duality between Cosserat elasticity and fractons

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