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Title: Lattice spin models for non-Abelian chiral spin liquids

Abstract

Here, we suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2) n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2) n gapless edge excitations.

Authors:
 [1];  [2]
  1. Univ. de Cergy-Pontoise, Cergy-Pontoise Cedex (France)
  2. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1357956
Alternate Identifier(s):
OSTI ID: 1353279
Report Number(s):
BNL-113800-2017-JA
Journal ID: ISSN 2469-9950; PRBMDO; R&D Project: PO015; KC0202030; TRN: US1702616
Grant/Contract Number:
SC00112704; AC02-98CH10886
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 14; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Lecheminant, P., and Tsvelik, A. M.. Lattice spin models for non-Abelian chiral spin liquids. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.95.140406.
Lecheminant, P., & Tsvelik, A. M.. Lattice spin models for non-Abelian chiral spin liquids. United States. doi:10.1103/PhysRevB.95.140406.
Lecheminant, P., and Tsvelik, A. M.. Wed . "Lattice spin models for non-Abelian chiral spin liquids". United States. doi:10.1103/PhysRevB.95.140406. https://www.osti.gov/servlets/purl/1357956.
@article{osti_1357956,
title = {Lattice spin models for non-Abelian chiral spin liquids},
author = {Lecheminant, P. and Tsvelik, A. M.},
abstractNote = {Here, we suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2)n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)n gapless edge excitations.},
doi = {10.1103/PhysRevB.95.140406},
journal = {Physical Review B},
number = 14,
volume = 95,
place = {United States},
year = {Wed Apr 26 00:00:00 EDT 2017},
month = {Wed Apr 26 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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  • In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less
  • In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less
  • In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less