Exactly solvable topological chiral spin liquid with random exchange

Chua, Victor; Fiete, Gregory A.

doi:10.1103/physrevb.84.195129

Cited by 18 publications

(19 citation statements)

References 38 publications

(47 reference statements)

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“…Agreeing with previous studies [46,47] on weak disorder (δJ < 1), Fig. 13 shows that the disorder averaged energy gap 0 decreases monotonously with increasing disorder strength δJ .…”

Section: Disorder In the Vortex-free Sectorsupporting

confidence: 88%

Perturbed vortex lattices and the stability of nucleated topological phases

2014

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We study the stability of nucleated topological phases that can emerge when interacting non-Abelian anyons form a regular array. The studies are carried out in the context of Kitaev's honeycomb model, where we consider three distinct types of perturbations in the presence of a lattice of Majorana mode binding vortices -spatial anisotropy of the vortices, dimerization of the vortex lattice and local random disorder. While all the nucleated phases are stable with respect to weak perturbations of each kind, strong perturbations are found to result in very different behavior. Anisotropy of the vortices stabilizes the strong-pairing like phases, while dimerization can recover the underlying non-Abelian phase. Local random disorder, on the other hand, can drive all the nucleated phases into a gapless thermal metal state. We show that all these distinct behavior can be captured by an effective staggered tight-binding model for the Majorana modes. By studying the pairwise interactions between the vortices, i.e. the amplitudes for the Majorana modes to tunnel between vortex cores, the locations of phase transitions and the nature of the resulting states can be predicted. We also find that due to oscillations in the Majorana tunneling amplitude, lattices of Majorana modes may exhibit a Peierls-like instability, where a dimerized configuration is favored over a uniform lattice. As the nature of the nucleated phases depends only on the Majorana tunneling, our results are expected to apply also to other system supporting localized Majorana mode arrays, such as Abrikosov lattices in p-wave superconductors, Wigner crystals in Moore-Read fractional quantum Hall states or arrays of topological nanowires.

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“…Agreeing with previous studies [46,47] on weak disorder (δJ < 1), Fig. 13 shows that the disorder averaged energy gap 0 decreases monotonously with increasing disorder strength δJ .…”

Section: Disorder In the Vortex-free Sectorsupporting

confidence: 88%

Perturbed vortex lattices and the stability of nucleated topological phases

2014

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“…[7] and [34], and a Kitaev-style chiral spin-liquid model with random exchange was considered in Ref. [35].) We shall utilize the Majoranafermion representation to investigate the magnetic response of the bond-disordered Kitaev spin liquid, in particular the NMR line shape.…”

Section: Introductionmentioning

confidence: 99%

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

Zschocke

Vojta

2015

Phys. Rev. B

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Kitaev's compass model on the honeycomb lattice realizes a spin liquid whose emergent excitations are dispersive Majorana fermions and static Z 2 gauge fluxes. We discuss the proper selection of physical states for finite-size simulations in the Majorana representation, based on a recent paper by F. L. Pedrocchi, S. Chesi, and D. Loss [Phys. Rev. B 84, 165414 (2011)]. Certain physical observables acquire large finite-size effects, in particular if the ground state is not fermion-free, which we prove to generally apply to the system in the gapless phase and with periodic boundary conditions. To illustrate our findings, we compute the static and dynamic spin susceptibilities for finite-size systems. Specifically, we consider random-bond disorder (which preserves the solubility of the model), calculate the distribution of local flux gaps, and extract the NMR line shape. We also predict a transition to a random-flux state with increasing disorder.

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“…1a). The existence of such delocalized quantum states can be demonstrated 44 with mathematical rigor using the theory of non-commutative Chern number, 64 while numerically, it has been demonstrated using recursive Green's function and transfer matrix calculations, 51,74,99,100 level statistics analysis, 44,67,101 simulations of the edge currents and computations of the edge conductance. [102][103][104] Near the transitions, the field-theoretic arguments developed by Pruisken and collaborators [105][106][107][108] for IQHE predict the T-driven flowdiagram shown in Fig.…”

Section: Quantum Criticality In the Spin-up Sector Of The Kane-mmentioning

confidence: 99%

Quantum criticality at the Chern-to-normal insulator transition

Xue

Prodan

2013

Phys. Rev. B

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Using the non-commutative Kubo formula for aperiodic solids and a recently developed numerical implementation, we study the conductivity σ and resistivity ρ tensors as functions of Fermi level E F and temperature T, for models of strongly disordered Chern insulators. The formalism enabled us to converge the transport coefficients at temperatures low enough to enter the quantum critical regime at the Chern-to-trivial insulator transition. We find that the ρ xx -curves at different temperatures intersect each other at one single critical point, and that they obey a single-parameter scaling law with an exponent close to the universally accepted value for the unitary symmetry class. However, when compared with the established experimental facts on the plateau-insulator transition in the Integer Quantum Hall Effect, we find a universal critical conductance σ c xx twice as large, an ellipse rather than a semi-circle law, and absence of the Quantized Hall Insulator phase.

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Exactly solvable topological chiral spin liquid with random exchange

Cited by 18 publications

References 38 publications

Perturbed vortex lattices and the stability of nucleated topological phases

Perturbed vortex lattices and the stability of nucleated topological phases

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

Quantum criticality at the Chern-to-normal insulator transition

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