On duality between Cosserat elasticity and fractons

Gromov, Andrey; Surówka, Piotr

doi:10.21468/scipostphys.8.4.065

Cited by 45 publications

(27 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, in certain fracton models, the restricted mobility of excitations can formally be understood as a consequence of the fact that the many-body dynamics conserves not only the total charge density of fractons, but also the total dipole moment (or higher multipole moment) associated with this charge [50][51][52]. Systems with such conservation laws naturally couple to symmetric tensor gauge theories [53][54][55], just like theories of classical or quantum elasticity [56][57][58][59][60][61][62][63][64][65][66][67]. Other fracton models are understood by duality to systems with subsystem symmetries [68].…”

Section: Introductionmentioning

confidence: 99%

Fracton hydrodynamics

Gromov

Lucas

Nandkishore

2020

Phys. Rev. Research

Self Cite

197

164

View full text Add to dashboard Cite

We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter. Fracton phases are characterized by elementary excitations (fractons) with restricted mobility. The hydrodynamic theories we introduce describe thermalization in systems with fractonlike mobility constraints, including fluids where charge and dipole moment are both locally conserved, and fluids where charge is conserved along every line or plane of a lattice. Each of these fluids is subdiffusive and constitutes a new universality class of hydrodynamic behavior. There are infinitely many such classes, each with distinct subdiffusive exponents, all of which are captured by our formalism. Our framework naturally explains recent results on dynamics with constrained quantum circuits, as well as recent experiments with ultracold atoms in tilted optical lattices. We identify crisp experimental signatures of these novel hydrodynamics and explain how they may be realized in near term ultracold atom experiments.

show abstract

Section: Introductionmentioning

confidence: 99%

Fracton hydrodynamics

Gromov

Lucas

Nandkishore

2020

Phys. Rev. Research

Self Cite

197

164

View full text Add to dashboard Cite

show abstract

“…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].…”

mentioning

confidence: 99%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

359

269

View full text Add to dashboard Cite

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.

show abstract

“…Using Eqs. (6.4), (6.5), we can solve the dynamical Ehrenfest constrain (6.6) by introducing an additional u(1) gauge field b µ [69,73]…”

Section: Vortex Crystalmentioning

confidence: 99%

“…Moreover, a disclination dipole is equivalent to a dislocation, with the Burgers vector perpendicular to the dipole moment. The duality has been generalized in several different directions and was used to revisit the melting transition in quantum crystals [70][71][72][73]. It was also generalized to three spatial dimensions [74] and to quantum smectic phases [75], that are dual to more general multipole theories studied in [76][77][78].…”

Section: Introductionmentioning

confidence: 99%

Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

2020

Self Cite

View full text Add to dashboard Cite

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

show abstract

On duality between Cosserat elasticity and fractons

Cited by 45 publications

References 61 publications

Fracton hydrodynamics

Fracton hydrodynamics

Fracton phases of matter

Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

Contact Info

Product

Resources

About