Anisotropic layer construction of anisotropic fracton models

Fuji, Yohei

doi:10.1103/physrevb.100.235115

Cited by 34 publications

(22 citation statements)

References 84 publications

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“…1) is similar to some constructions of SPT and SET phases [45][46][47][48]. It is also similar to the layer, cage-net, or string-membrane constructions of fracton phases [49][50][51][52][53][54]. However, there are some important differences, which allow us to construct new fracton states with fractal excitations [22], even starting from 2 + 1D Z 2 topological order.…”

Section: Introductionsupporting

confidence: 53%

Systematic construction of gapped nonliquid states

Wen

2020

Phys. Rev. Research

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Using Abelian and non-Abelian topological orders in two-dimensional (2D) space and the different ways to glue them together via their gapped boundaries, we propose a systematic way to construct three-dimensional (3D) gapped states (and in other dimensions). The resulting states are called cellular topological states, which include gapped nonliquid states, as well as gapped liquid states in some special cases. Some new fracton states with fractal excitations are constructed even using 2D Z 2 topological order. More general cellular topological states can be constructed by connecting 2D domain walls between different 3D topological orders. The constructed cellular topological states can be viewed as fixed-point states for a reverse renormalization of gapped nonliquid states.

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Section: Introductionsupporting

confidence: 53%

Systematic construction of gapped nonliquid states

Wen

2020

Phys. Rev. Research

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“…Amazingly, this model, in different limits, displays either 3D fracton order or supports a Z 2 spin liquid phase.Thanks to the rapid development of the Kitaev materials discovered in correlated spin orbital coupled system including N a 2 IrO 3 , α-Li 2 IrO 3 , α-RuCl 3 and H 3 LiIr 2 O 6 , we expect there may exist a material candidate for such a fracton phase. There have also been recent simplifications to the Slagle-Kim construction which are promising for material realization[77]. Additionally, synthetic quantum matter, such as AMO experiments, provide another possible route to the experimental realization of fracton phases.Apart from the gapped fracton topological ordered state represented by stabilizer codes, there has also been a parallel search on gapless fracton phases whose low energy effective theory is characterized by tensor gauge theories.…”

mentioning

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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“…Fracton topological order, originally constructed in lattice spin models [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and later on extended to the scope of continuum field theories [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], is characterized by a gapped spectrum with quasiparticle excitations with either restricted mobility (type-I fractons) or no mobility at all (type-II fractons), and a ground state degeneracy (GSD) that depends not only on the topology of the manifold but also on the geometry of the lattice. This dependence on the lattice details signals a sort of ultraviolet/infrared (UV/IR) mixing, i.e., fracton systems do not present the usual decoupling between high and low-energy physical properties.…”

Section: Introductionmentioning

confidence: 99%

Field Theories for type-II fractons

2022

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We derive an effective field theory for a type-II fracton starting from the Haah code on the lattice. The effective topological theory is not given exclusively in terms of an action; it must be supplemented with a condition that selects physical states. Without the constraint, the action only describes a type-I fracton. The constraint emerges from a condition that cube operators multiply to the identity, and it cannot be consistently implemented in the continuum theory at the operator level, but only in a weaker form, in terms of matrix elements of physical states. Informed by these studies and starting from the opposite end, i.e., the continuum, we discuss a Chern-Simons-like theory that does not need a constraint or projector, and yet has no mobile excitations. Whether this continuum theory admits a lattice counterpart remains unanswered.

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Anisotropic layer construction of anisotropic fracton models

Cited by 34 publications

References 84 publications

Systematic construction of gapped nonliquid states

Systematic construction of gapped nonliquid states

Fracton phases of matter

Field Theories for type-II fractons

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