Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands

Ebisu, Hiromi; Kalloor, Rohit R.; Tsvelik, A. M.; Oreg, Yuval

doi:10.1103/physrevb.102.165112

Cited by 3 publications

(1 citation statement)

References 69 publications

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“…However, there is yet another class of exactly solvable models defined on an array of one-dimensional (1d) quantum wires, where one direction is continuum whereas the other directions are discrete. This so-called coupledwire construction [68] has been successfully applied to 2d topological phases, including chiral ones, such as fractional quantum Hall states [69][70][71][72][73][74][75][76][77][78][79][80] and quantum spin liquids [81][82][83][84][85][86][87][88][89][90]. With the helps of bosonization technique and conformal field theory (CFT) [91][92][93][94][95], this construction yields exactly solvable models in the strong-coupling limit and allows us to study universal features of topological order.…”

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confidence: 99%

Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders

Fuji¹,

Furusaki²

2021

Preprint

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Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lowerdimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy. Furthermore, we apply this construction to two-dimensional coupled-wire models with ordinary topological orders and translation symmetry enriched topological orders. Our results pave the way for effective quantum field descriptions or microscopic model realizations of fracton orders with chiral gapless surface states.

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