Foliated fracton order from gauging subsystem symmetries

Shirley, Wilbur; Slagle, Kevin; Xie, Changsheng

doi:10.21468/scipostphys.6.4.041

Cited by 139 publications

(113 citation statements)

References 60 publications

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“…19 with red (green) sites at top and bottom and four green (red) sites in between. Thus, our construction exactly reproduces the planon-lineon model [38] whose elementary quasiparticles are lineons and planons with mobility restricted to the z-direction and the xz (yz)-planes, respectively.…”

Section: A Majorana Islandsmentioning

confidence: 60%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

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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 Majorana Islandsmentioning

confidence: 60%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

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343

269

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“…A new chapter in the book of three-dimensional (3D) quantum phases of matter was opened with the discovery of fracton models [1][2][3][4][5][6][7][8], characterized by the presence of topological excitations with restricted mobility. These peculiar particles have attracted significant recent interest, thereby revealing intriguing connections to quantum information processing [9][10][11][12], topological order [13][14][15][16][17][18][19][20][21][22], sub-system symmetries [23][24][25][26][27][28][29][30], and slow quantum dynamics [1,3,[31][32][33]. Much of the phenomenology of fractons can also be realized in tensor gauge theories [34][35][36][37][38][39][40][41][42][43][44] with higher moment conservation laws, unveiling further connections of fractons with elasticity …”

Section: Introductionmentioning

confidence: 99%

Gauging permutation symmetries as a route to non-Abelian fractons

Prem

Williamson

2019

SciPost Phys.

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We discuss the procedure for gauging on-site Z 2 global symmetries of threedimensional lattice Hamiltonians that permute quasi-particles and provide general arguments demonstrating the non-Abelian character of the resultant gauged theories. We then apply this general procedure to lattice models of several well known fracton phases: two copies of the X-Cube model, two copies of Haah's cubic code, and the checkerboard model. Where the former two models possess an on-site Z 2 layer exchange symmetry, that of the latter is generated by the Hadamard gate. For each of these models, upon gauging, we find non-Abelian subdimensional excitations, including non-Abelian fractons, as well as non-Abelian looplike excitations and Abelian fully mobile pointlike excitations. By showing that the looplike excitations braid non-trivially with the subdimensional excitations, we thus discover a novel gapped quantum order in 3D, which we term a "panoptic" fracton order. This points to the existence of parent states in 3D from which both topological quantum field theories and fracton states may descend via quasi-particle condensation. The gauged cubic code model represents the first example of a gapped 3D phase supporting (inextricably) non-Abelian fractons that are created at the corners of fractal operators. Contents B Gauging the Hadamard symmetry of the 2D color code 30References 33 1 Here, by subdimensional we refer to excitations that are fully immobile (fractons), mobile only along lines (lineons), or mobile only along planes (planons) of the 3D lattice.2 Non-Abelian excitations are those which participate in multiple fusion channels and can thus encode quantum information non-locally throughout the system. See e.g., Refs. [77,78]. 3 We interchangeably refer to this global symmetry as swap, layer-swap, or layer exchange symmetry. 4 This gauging technique, when applied to two copies of a quantum double D(G), leads to a model in the same phase as D(G), withG = (G × G) Z2 which is non-Abelian even when the underlying group G is Abelian.

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“…Thus, the ground state degeneracy is proportional to 2 number of geodesics , which is also proportional to 2 boundary size . This feature is dubbed "subsystem symmetry" in literature [7,16,27]. It is a symmetry in-between local and global, and the origin of many exotic features of fracton models, including the holographic ones.…”

Section: Brief Review Of the Holographic Hyperbolic Fracton Modelmentioning

confidence: 99%

“…Formulated in the language of arrows and vertices, it has the advantage of illuminating various connections between the hyperbolic fracton model and other established results in fracton phases and holography. In this section, we will describe the dual eight-vertex model, and discuss how it works as a straightforward demonstration of fracton-elasticity duality [37,39,40] and subsystem charge [27].…”

Section: Dual Eight Vertex Model On the Square Latticementioning

confidence: 99%

Hyperbolic fracton model, subsystem symmetry, and holography. II. The dual eight-vertex model

Han

2019

Phys. Rev. B

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The discovery of fracton states of matter opens up an exciting, largely unexplored field of manybody physics. Certain fracton states' similarity to gravity is an intriguing property. In an earlier work [1], we have demonstrated that a simple fracton model in anti-de Sitter space satisfies several major holographic properties. In this follow-up paper, we study the eight-vertex model dual to the original model. The dual model has the advantage of illuminating the mutual information and subsystem charges pictorially, which helps to reveal its connections to various other topics in the study of holography and fracton phases. At zero temperature, the dual eight-vertex model is a discrete realization of the bit-thread model, a powerful tool developed to visualize holography. The bit-thread picture combined with subsystem charges can give a quantitative account of the isometry between the bulk and the boundary at finite energy, which is also a key issue for holography. The black hole microscopic degrees of freedom can be identified in this picture, which turn out to be encoded non-locally on the horizon. The eight-vertex model proves to be a very helpful venue to improve our understanding of the hyperbolic fracton model as a toy model of holography.

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Foliated fracton order from gauging subsystem symmetries

Cited by 139 publications

References 60 publications

Fracton phases of matter

Fracton phases of matter

Gauging permutation symmetries as a route to non-Abelian fractons

Hyperbolic fracton model, subsystem symmetry, and holography. II. The dual eight-vertex model

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