RVB gauge theory and the topological degeneracy in the honeycomb Kitaev model
type: Item
instance of: scholarly article
title: RVB gauge theory and the topological degeneracy in the honeycomb Kitaev model
zbMATH Open document ID: 1269.81170
DOI: 10.1088/1751-8113/45/33/335304
published in: Journal of Physics A: Mathematical and Theoretical
publication date: 2012-09-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1111.3813
Mathematics Subject Classification ID: 81T45
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 82B23
Mathematics Subject Classification ID: 82D80
Mathematics Subject Classification ID: 81T25
Mathematics Subject Classification ID: 81R25
zbMATH DE Number: 6081373
zbMATH Keywords: resonating valence bond states
zbMATH Keywords: Kitaev model, SU(2) gauge theory, Jordan-Wigner transformation
MaRDI profile type: Publication
OpenAlex ID: W3103281801
arXiv ID: 1111.3813
author: S. Mandal
author: R. Shankar
author: G. Baskaran
review text: In the search for unconventional, anyonic excitations of two-dimensional quantum spin models (with as yet more or less speculative applications to high-temperature superconductivity, fractional quantum Hall effect and quantum computers), Kitaev introduced a model on the honeycomb lattice with exactly solvable spectrum, reducible to a local SU(2)-gauge theory. The model may be re-expressed in terms of Majorana fermions, including gauge-invariant fermions, and gauge operators, quadratic in the fermions, which are only invariant under the center \(\mathbb Z_2\) of \(SU(2)\). The remaining \(\mathbb Z_2\)-gauge symmetry may be essentially quotiented out by the choice of a Jordan-Wigner fermionization along a covering, non-intersecting path. The Hamiltonian (38) is then a quadratic form in Majorana fermions \(\eta\) with coefficients \(\pm 1\) along normal bounds. The ground state is known independently to correspond to configurations which are flux-free on every plaquette; this leaves open the problem of fixing the value of the Wilson loop along two generators of the covering group of the two-torus (also called large gauge transformations), and leads to a four-fold degeneracy of the ground state. On the other hand, through the Jordan-Wigner fermionization, the constraint on the flux is shown to leave out four sectors, in each of which the Hamiltonian is explicitly diagonalizable, giving a new, algebraic proof of the four-fold degeneracy of the ground state. The article proceeds further to prove four-fold degeneracy of \textit{any} eigenstate by exhibiting in the Jordan-Wigner realization four explicit operators changing the value of the Wilson loop associated to the large gauge transformations without changing the values of the fluxes.
reviewed by: Jeremie Unterberger
description: scientific article; zbMATH DE number 6081373