Fracton-like phases from subsystem symmetries

Ibieta-Jimenez, J. P.; Xavier, L. N. Queiroz; Petrucci, M.; Teotonio-Sobrinho, P.

doi:10.48550/arxiv.1908.07601

Cited by 2 publications

(2 citation statements)

References 63 publications

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“…Finally, we note that there have been numerous other constructions of fracton spin models which we have not had space to discuss here [80][81][82].…”

Section: Towards Realistic Spin Modelsmentioning

confidence: 99%

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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“…Finally, we note that there have been numerous other constructions of fracton spin models which we have not had space to discuss here [80][81][82].…”

Section: Towards Realistic Spin Modelsmentioning

confidence: 99%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

343

269

View full text Add to dashboard Cite

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“…Although initially of interest for their potential as self-correcting quantum memories [9][10][11], three dimensional (3+1D) gapped fracton models have recently been shown to harbor intriguing connections with topological order [12][13][14][15][16][17][18], slow quantum dynamics [2,3,19,20], subsystem symmetries [8,[21][22][23][24][25][26][27], and quantum information processing [28]. Fractonic matter, however, is defined more broadly as including any (not necessarily gapped) quantum phase of matter with restricted mobility excitations (that are not necessarily topological), examples of which by now abound.…”

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confidence: 99%

Topological Defect Networks for Fractons of all Types

Aasen,

Bulmash,

Prem

et al. 2020

Preprint

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Fracton phases exhibit striking behavior which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter. Here, we explore fracton phases from the perspective of defect TQFTs and show that topological defect networks-networks of topological defects embedded in stratified 3+1D TQFTs-provide a unified framework for describing various types of gapped fracton phases. In this picture, the sub-dimensional excitations characteristic of fractonic matter are a consequence of mobility restrictions imposed by the defect network. We conjecture that all gapped phases, including fracton phases, admit a topological defect network description and support this claim by explicitly providing such a construction for many well-known fracton models, including the X-Cube and Haah's B code. To highlight the generality of our framework, we also provide a defect network construction of a novel fracton phase hosting non-Abelian fractons. As a byproduct of this construction, we obtain a generalized membrane-net description for fractonic ground states as well as an argument that our conjecture implies no type-II topological fracton phases exist in 2+1D gapped systems. Our work also sheds light on new techniques for constructing higher order gapped boundaries of 3+1D TQFTs. CONTENTS III. Haah's B Code from TopologicalDefects 9 A. Review of Haah's B code 9 B. Condensation on defects 9 C. Nets and relations 12 IV. Non-Abelian fracton model from topological defects in 3+1D D 4 gauge theory 12 A. Review of D 4 gauge theory 13 B. Condensation on defects 13 C. Mobility constraints 14 D. Nets and relations 15 E. Relation to other models 15 V. Classifying phases with topological defect networks 16 A. No type-II fractons in 2+1D 16 B. Phase preserving defect network equivalences 17 VI. Conclusion References A. Field Theory B. Fractal-like Lineon Model C. Z 3 type-I fracton model from coupled 2+1D layers D. X-Cube from defects lattice model E. Lattice model for B code from defects F. Lattice Hamiltonian for non-Abelian defect model 1. Brief review of 3+1D Lattice Gauge Theory 2. D 4 defect Hamiltonian 3. The 1-strata defect in the net-basis

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Fracton-like phases from subsystem symmetries

Cited by 2 publications

References 63 publications

Fracton phases of matter

Fracton phases of matter

Topological Defect Networks for Fractons of all Types

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