Strong planar subsystem symmetry-protected topological phases and their dual fracton orders

Devakul, Trithep; Shirley, Wilbur; Wang, Juven

doi:10.1103/physrevresearch.2.012059

Cited by 52 publications

(31 citation statements)

References 82 publications

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“…The toy model we introduce here is a subsystem symmetric topological state [131][132][133][134][135][136] with gapless edge modes, which we refer to as topological plaquette Ising model (TPIM).…”

Section: Subsystem Symmetry Protected Topological Phasesmentioning

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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Section: Subsystem Symmetry Protected Topological Phasesmentioning

confidence: 99%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

343

269

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“…A new paradigm in the classification of gapped phases of matter has recently begun thanks to the discovery of models with novel subdimensional physics. This includes the fracton topological phases [1][2][3][4][5][6][7][8][9][10][11][12], in which topological quasiparticles are either immobile or confined to move only within subsystem such as lines or planes, as well as models with subsystem symmetries, which are symmetries that act nontrivially only on rigid subsystems of the entire system [7,8,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. These two types of models are dual since gauging subsystem symmetries can result in fracton topological order, analogous to how topological order can be obtained by gauging a global symmetry [7,8,15].…”

Section: Introductionmentioning

confidence: 99%

“…Models with subsystem symmetries are also interesting in their own right. For example, one may use them to define symmetry-protected topological (SPT) phases, giving rise to the so-called subsystem SPT (SSPT) phases [16][17][18][19][20][21][22]26,28]. SSPT phases display new physics compared to conventional SPT phases such as extensive edge degeneracy and unique entanglement properties.…”

Section: Introductionmentioning

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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“…Several classifications of subsystem symmetry protected phases have been proposed [38][39][40][41]. Some of these classifications have been based on the twist phase, a topological invariant related to the projective representations of the symmetry group.…”

Section: B Subsystem Symmetrymentioning

confidence: 99%

“…Analogously, while there are no frac-ton topological phases in 2D spin systems [36,37], there are nontrivial SSPT phases that exhibit similar topological phenomena with respect to subsystem symmetric operators [22,23]. To date, the classification of these phases has garnered significant interest and ample progress [38][39][40][41] but a consensus has not been reached. This raises a natural question: What is the nature of the flows generated by SSPTs under subsystem symmetry-preserving ERG?…”

Section: Introductionmentioning

confidence: 99%

Bifurcating subsystem symmetric entanglement renormalization in two dimensions

2021

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We introduce the subsystem symmetry-preserving real-space entanglement renormalization group and apply it to study bifurcating flows generated by linear and fractal subsystem symmetry-protected topological phases in two spatial dimensions. We classify all bifurcating fixed points that are given by subsystem symmetric cluster states with two qubits per unit cell. In particular, we find that the square lattice cluster state is a quotient-bifurcating fixed point, while the cluster states derived from Yoshida's first-order fractal spin liquid models are self-bifurcating fixed points. We discuss the relevance of bifurcating subsystem symmetry-preserving renormalization group fixed points for the classification and equivalence of subsystem symmetry-protected topological phases.

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Strong planar subsystem symmetry-protected topological phases and their dual fracton orders

Cited by 52 publications

References 82 publications

Fracton phases of matter

Fracton phases of matter

Subsystem symmetry enriched topological order in three dimensions

Bifurcating subsystem symmetric entanglement renormalization in two dimensions

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