DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Model of spin liquids with and without time-reversal symmetry

Journal Article · · Physical Review B
 [1];  [1];  [2]; ORCiD logo [3]
  1. Paul Scherrer Inst. (PSI), Villigen (Switzerland)
  2. Boston Univ., MA (United States)
  3. Brookhaven National Lab. (BNL), Upton, NY (United States)

We study a model in (2 + 1)-dimensional space-time that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1 + 1)-dimensional space-time, coupled via current-current interactions. The model is shown to have a lattice realization as an array of coupled quantum spin-1/2 ladders. We study this model both in the presence and in the 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 for which a nonchiral gapless non-Abelian spin liquid is stable. The excitations in this regime are described by relativistic Majorana fields in (2 + 1)-dimensional space-time, much as those appearing in the Kitaev honeycomb model but here emerging in a model of coupled spin ladders that do not break the SU(2) spin-rotation symmetry

Research Organization:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0012704; FG02-06ER46316
OSTI ID:
1543410
Alternate ID(s):
OSTI ID: 1523551
Report Number(s):
BNL-211895-2019-JAAM; PRBMDO
Journal Information:
Physical Review B, Vol. 99, Issue 18; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

References (55)

Equivalence of the resonating-valence-bond and fractional quantum Hall states journal November 1987
Topological Orders and Chern-Simons Theory in Strongly Correlated Quantum Liquid journal June 1991
Anyons in an exactly solved model and beyond journal January 2006
Nonabelions in the fractional quantum hall effect journal August 1991
Crossed sliding Luttinger liquid phase journal February 2001
Fractional Quantum Hall Effect in an Array of Quantum Wires journal January 2002
From Luttinger liquid to non-Abelian quantum Hall states journal February 2014
Pairing in Luttinger Liquids and Quantum Hall States journal July 2017
Coupled wire model of Z 4 orbifold quantum Hall states journal August 2018
Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states journal June 1990
Chiral spin liquids in arrays of spin chains journal June 2015
Non-Abelian topological spin liquids from arrays of quantum wires or spin chains journal May 2016
Lattice spin models for non-Abelian chiral spin liquids journal April 2017
Coupled spin- 1 2 ladders as microscopic models for non-Abelian chiral spin liquids journal April 2017
Model of chiral spin liquids with Abelian and non-Abelian topological phases journal December 2017
Gapless chiral spin liquid from coupled chains on the kagome lattice journal January 2018
Chiral spin states and superconductivity journal June 1989
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect journal April 2000
Non-Abelian Statistics of Half-Quantum Vortices in p -Wave Superconductors journal January 2001
Successive Majorana topological transitions driven by a magnetic field in the Kitaev model journal August 2018
Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models journal January 2009
Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections journal March 2018
Simple Fermionic Model of Deconfined Phases and Phase Transitions journal December 2016
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" journal October 1988
Quantum Field Theory in Condensed Matter Physics book January 2010
Braid Statistics in Local Quantum Theory journal January 1990
Density matrix formulation for quantum renormalization groups journal November 1992
Density-matrix algorithms for quantum renormalization groups journal October 1993
Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains journal April 1996
One-Dimensional Spin-Liquid without Magnon Excitations journal May 1997
Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model journal February 1983
Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State journal April 1983
Melting of a frustration-induced dimer crystal and incommensurability in the J 1 - J 2 two-leg ladder journal October 2011
Entanglement entropy and conformal field theory journal December 2009
Boundary Effects in the Critical Scaling of Entanglement Entropy in 1D Systems journal March 2006
Entanglement entropy in quantum impurity systems and systems with boundaries journal December 2009
Unusual corrections to scaling in entanglement entropy journal April 2010
Field-theory treatment of the Heisenberg spin-1 chain journal December 1990
Dimerized Phase and Transitions in a Spatially Anisotropic Square Lattice Antiferromagnet journal September 2004
Ordering in Spatially Anisotropic Triangular Antiferromagnets journal February 2007
Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study journal November 2018
Quantum Field Theory in Condensed Matter Physics journal February 1997
Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections text January 2018
From Luttinger liquid to non-Abelian quantum Hall states text January 2011
Chiral Spin Liquids in Arrays of Spin Chains text January 2015
Pairing in Luttinger Liquids and Quantum Hall States text January 2017
A model of chiral spin liquids with Abelian and non-Abelian topological phases text January 2017
Successive Majorana Topological Transitions Driven by a Magnetic Field in the Kitaev Model text January 2018
Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders text January 2018
Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study text January 2018
Non-abelian statistics of half-quantum vortices in p-wave superconductors text January 2000
Anyons in an exactly solved model and beyond text January 2005
Ordering in spatially anisotropic triangular antiferromagnets text January 2006
Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains text January 1995
One-dimensional spin-liquid without magnon excitations text January 1996

Cited By (2)