Compactifying fracton stabilizer models

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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“…See also Ref. [88] for a discussion of calculating invariants for fracton phases based on compactification.…”

Section: Twisted Phasesmentioning

confidence: 99%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

359

269

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“…To formalize this, we can use the language of group cohomology which classifies SPT order. Imagine "compactifying" our 3D system into a quasi-2D system [60]. This is achieved simply by fixing the length R in the y direction, as indicated in Fig.…”

Section: Boundary Of the Ssptmentioning

confidence: 99%

Subsystem symmetry enriched topological order in three dimensions

Stephen

Garre-Rubio

Dua

et al. 2020

Phys. Rev. Research

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We introduce a model of three-dimensional (3D) topological order enriched by planar subsystem symmetries. The model is constructed starting from the 3D toric code, whose ground state can be viewed as an equal-weight superposition of two-dimensional (2D) membrane coverings. We then decorate those membranes with 2D cluster states possessing symmetry-protected topological order under linelike subsystem symmetries. This endows the decorated model with planar subsystem symmetries under which the looplike excitations of the toric code fractionalize, resulting in an extensive degeneracy per unit length of the excitation. We also show that the value of the topological entanglement entropy is larger than that of the toric code for certain bipartitions due to the subsystem symmetry enrichment. Our model can be obtained by gauging the global symmetry of a short-range entangled model which has symmetry-protected topological order coming from an interplay of global and subsystem symmetries. We study the nontrivial action of the symmetries on boundary of this model, uncovering a mixed boundary anomaly between global and subsystem symmetries. To further study this interplay, we consider gauging several different subgroups of the total symmetry. The resulting network of models, which includes models with fracton topological order, showcases more of the possible types of subsystem symmetry enrichment that can occur in 3D.

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“…if the crystalline unit cell is enlarged, and can be used to study distinctions between phases that are preserved or lost upon such lowering of symmetry. A number of other works have also investigated the interplay between lattice geometry or symmetry and fracton order, from a variety of perspectives [30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Fracton fusion and statistics

Pai

Hermele

2019

Phys. Rev. B

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We introduce and develop a theory of fusion and statistical processes of gapped excitations in Abelian fracton phases. The key idea is to incorporate lattice translation symmetry via its action on superselection sectors, which results in a fusion theory endowed with information about the non-trivial mobility of fractons and sub-dimensional excitations. This results in a description of statistical processes in terms of local moves determined by the fusion theory. Our results can be understood as providing a characterization of translation-invariant fracton phases. We obtain simple descriptions of the fusion theory in the X-cube and checkerboard fracton models, as well as for gapped electric and magnetic excitations of some gapless U(1) tensor gauge theories. An alternate route to the X-cube model fusion theory is provided by starting with a system of decoupled twodimensional toric code layers, and giving a description of the p-string condensation mechanism within our approach. We discuss examples of statistical processes of fractons and sub-dimensional excitations in the X-cube and checkerboard models. As an application of the ideas developed, we prove that the X-cube and semionic X-cube models realize distinct translation-invariant fracton phases, even when the translation symmetry is broken corresponding to an arbitrary but finite enlargement of the crystalline unit cell. CONTENTS

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Compactifying fracton stabilizer models

Cited by 33 publications

References 125 publications

Fracton phases of matter

Fracton phases of matter

Subsystem symmetry enriched topological order in three dimensions

Fracton fusion and statistics

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