Model of chiral spin liquids with Abelian and non-Abelian topological phases

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; Tsvelik, A. M.

doi:10.1103/physrevb.96.224420

Cited by 25 publications

(31 citation statements)

References 33 publications

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“…which may be generated by four-spin interactions, such as S + r,1 S + r,2 S − r ,1 S − r ,2 . However, we remark that these interactions are irrelevant for the SU (2)-symmetric spin chains, in contrast to similar microscopic constructions for the 2D case where interactions are marginal [62][63][64], since J l r has the weight h = 1 and thus the interactions have the scaling dimension 4. In principle, they can be made relevant by adding appropriate forward scattering interactions to H 0 [25], but we do not pursue their detailed microscopic forms at this stage.…”

mentioning

confidence: 77%

From coupled wires to coupled layers: Model with three-dimensional fractional excitations

Fuji

Furusaki

2019

Phys. Rev. B

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We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)dimensional conformal field theory (CFT) associated with a current algebra g. The wires are coupled with each other to form a 3D network through the current-current interactions of g1 and g2 CFTs that are related to the g CFT by a nontrivial conformal embedding g ⊃ g1 × g2. The resulting model can be viewed as a layer construction of a 3D topologically ordered state, in which the conformal embedding in each wire implements the anyon condensation between adjacent layers. Local operators acting on the ground state create point-like or loop-like deconfined excitations depending on the branching rule. We demonstrate our construction for a simple solvable model based on the conformal embedding SU (2)1 × SU (2)1 ⊃ U (1)4 × U (1)4. We show that the model possesses extensively degenerate ground states on a torus with deconfined quasiparticles, and that appropriate local perturbations lift the degeneracy and yield a 3D Z2 gauge theory with a fermionic Z2 charge.Introduction.-Two-dimensional (2D) topologically ordered phases, such as fractional quantum Hall states [1,2] and the toric codes [3], harbor deconfined quasiparticle excitations obeying nontrivial braiding statistics [4]. In three-dimensional (3D) space, topologically ordered phases can have two types of deconfined quasiparticles: point-like or loop-like. While the statistics between point-like quasiparticles can only be bosonic or fermionic in 3D space, there are possibilities of nontrivial pointloop, loop-loop, three-loop, and loop-loop-point braiding statistics [5][6][7][8][9][10][11]. Along with the development of mathematical frameworks for classifying topologically ordered phases [12][13][14][15][16], construction of microscopic Hamiltonians is also desired for their realizations in the real world. For certain 2D topological orders, a systematic construction scheme of exactly solvable Hamiltonians has been proposed by Levin and Wen in their string-net models [17]. Although our understanding of the 3D topological orders is much more limited, there have been several proposed schemes to write down exactly solvable Hamiltonians such as the Dijkgraaf-Witten model [18,19], the Walker-Wang model [20][21][22], and their relatives [23].In this Rapid Communication, we propose yet another way to construct microscopic Hamiltonians for 3D topologically ordered phases. Our approach is based on two key ingredients. The first one is coupled-wire construction of 2D topological phases originally developed by Kane and co-workers [24,25]. This construction uses a hybrid of continuum and lattice descriptions: One spatial direction is a discrete lattice, while the other direction is continuum and described by (1 + 1)-dimensional conformal field theory (CFT) [26]. It has been successfully applied to various 2D topological phases [27][28][29][30][31][32][33][34][35][36][37], and there have been sever...

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confidence: 77%

From coupled wires to coupled layers: Model with three-dimensional fractional excitations

Fuji

Furusaki

2019

Phys. Rev. B

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“…In Ref. 15 we studied the case λ = 0, λ = 0, which maximally breaks time-reversal symmetry (TRS). This limit was analyzed using mean-field theory and a random phase approximation that started from an exactly solvable limit.…”

Section: Motivation and Summary Of Resultsmentioning

confidence: 99%

“…We then couple consecutive ladders by considering interladder quartic interactions with real valued coupling constants λ and λ 15. This regime corresponds (with the singlet mass m s = 0) to the planar region (λ ≥ 0, λ = 0, m t > 0, m s = 0) in Fig.…”

Section: A Definitionmentioning

confidence: 99%

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Model of spin liquids with and without time-reversal symmetry

et al. 2019

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We study a model in (2+1)-dimensional spacetime that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1+1)-dimensional spacetime, coupled via currentcurrent interactions. The model is shown to have a lattice realization in an array of two-leg quantum spin-1/2 ladders. We study the model both in the presence and absence of time-reversal symmetry, within a mean-field approximation. We find regimes in coupling space where Abelian and non-Abelian spin liquid phases are stable. In the case when the Hamiltonian is time-reversal symmetric, we find regimes where gapped Abelian and non-Abelian chiral phases appear as a result of spontaneous breaking of time-reversal symmetry. These gapped phases are separated by a discontinuous phase transition. More interestingly, we find a regime where a non-chiral gapless non-Abelian spin liquid is stable. The excitations in this regime are described by relativistic Majorana fields in (2+1)dimensional spacetime, much as those appearing in the Kitaev honeycomb model, but here emerging in a model of coupled spin ladders that does not break SU (2) spin-rotation symmetry. CONTENTS

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“…This general pattern is explicitly confirmed in the work of ref. [22], where it is analyzed a mean field solution for a system of quantum wires built up from Majorana fermions with interactions sharing some features of that ones in (2.23).…”

Section: Case λ/G ≪mentioning

confidence: 99%

Effective theories for 2+1 dimensional non-Abelian topological spin liquids

Hernaski

Gomes

2017

J. High Energ. Phys.

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In this work we propose an effective low-energy theory for a large class of 2+1 dimensional non-Abelian topological spin liquids whose edge states are conformal degrees of freedom with central charges corresponding to the coset structure su(2) k ⊕ su(2) k ′ /su(2) k+k ′ . For particular values of k ′ it furnishes the series for unitary minimal and superconformal models. These gapped phases were recently suggested to be obtained from an array of one-dimensional coupled quantum wires. In doing so we provide an explicit relationship between two distinct approaches: quantum wires and Chern-Simons bulk theory. We firstly make a direct connection between the interacting quantum wires and the corresponding conformal field theory at the edges, which turns out to be given in terms of chiral gauged WZW models. Relying on the bulk-edge correspondence we are able to construct the underlying non-Abelian Chern-Simons effective field theory.

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Model of chiral spin liquids with Abelian and non-Abelian topological phases

Cited by 25 publications

References 33 publications

From coupled wires to coupled layers: Model with three-dimensional fractional excitations

From coupled wires to coupled layers: Model with three-dimensional fractional excitations

Model of spin liquids with and without time-reversal symmetry

Effective theories for 2+1 dimensional non-Abelian topological spin liquids

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