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

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

Abstract

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, the 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.

Authors:

Chen, Jyong-Hao ^[1]; Mudry, Christopher ^[1]; Chamon, Claudio ^[2]; Tsvelik, A. M. ^[3]

Paul Scherrer Inst. (PSI), Villigen (Switzerland). Condensed Matter Theory Group
Boston Univ., MA (United States). Dept. of Physics
Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Division

Publication Date:: 2017-12-15

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Swiss National Science Foundation (SNSF); Boston Univ., MA (United States)

OSTI Identifier:: 1425001

Alternate Identifier(s):: OSTI ID: 1413563; OSTI ID: 1425000

Report Number(s):: BNL-114843-2017-JAAM; BNL-114836-2017-JAAM
Journal ID: ISSN 2469-9950; PRBMDO; TRN: US1801993

Grant/Contract Number:: SC0012704; 2000021 153648; FG02-06ER46316; AC02-98CH10886

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 96; Journal Issue: 22; 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


                    Chen, Jyong-Hao, Mudry, Christopher, Chamon, Claudio, and Tsvelik, A. M. Model of chiral spin liquids with Abelian and non-Abelian topological phases.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevB.96.224420.

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                    Chen, Jyong-Hao, Mudry, Christopher, Chamon, Claudio, & Tsvelik, A. M. Model of chiral spin liquids with Abelian and non-Abelian topological phases.  United States.  https://doi.org/10.1103/PhysRevB.96.224420

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                    Chen, Jyong-Hao, Mudry, Christopher, Chamon, Claudio, and Tsvelik, A. M. Fri .  
"Model of chiral spin liquids with Abelian and non-Abelian topological phases".  United States.  https://doi.org/10.1103/PhysRevB.96.224420.  https://www.osti.gov/servlets/purl/1425001.

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@article{osti_1425001,

  title        = {Model of chiral spin liquids with Abelian and non-Abelian topological phases},

  author       = {Chen, Jyong-Hao and Mudry, Christopher and Chamon, Claudio and Tsvelik, A. M.},

  abstractNote = {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, the 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.},

  doi          = {10.1103/PhysRevB.96.224420},

  journal      = {Physical Review B},

  number       = 22,

  volume       = 96,

  place        = {United States},

  year         = {2017},

  month        = {12}

}

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Works referenced in this record:

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Works referencing / citing this record:

Exact solution of an integrable anisotropic $\boldsymbol{J_1-J_2}$ spin chain model
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Qiao, Yi; Sun, Pei; Xin, Zhirong
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Model of spin liquids with and without time-reversal symmetry
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Title: Model of chiral spin liquids with Abelian and non-Abelian topological phases

Abstract

Citation Formats

Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order journal, October 2010

Fate of spinons in spontaneously dimerized spin- 1 2 ladders journal, April 2000

Non-Abelian topological spin liquids from arrays of quantum wires or spin chains journal, May 2016

Interaction effect on topological classification of superconductors in two dimensions journal, August 2013

Anyons in an exactly solved model and beyond journal, January 2006

Weakly coupled one-dimensional Mott insulators journal, March 2002

The nonlinear sigma model and spin ladders journal, June 1996

Form factors of soliton-creating operators in the sine-Gordon model journal, July 2001

From Luttinger liquid to non-Abelian quantum Hall states journal, February 2014

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model journal, February 2001

Some properties of the model in two dimensions journal, September 1978

The S-matrix of the kinks of the model journal, September 1978

Correlation Lengths in Quantum Spin Ladders journal, May 1997

Theory of (2+1)-dimensional fermionic topological orders and fermionic/bosonic topological orders with symmetries journal, October 2016

Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains journal, April 1996

Chiral spin liquids in arrays of spin chains journal, June 2015

Detecting Topological Order in a Ground State Wave Function journal, March 2006

Dimensional Crossover in Quantum Antiferromagnets journal, November 1996

Topological Entanglement Entropy journal, March 2006

Coupled spin- 1 2 ladders as microscopic models for non-Abelian chiral spin liquids journal, April 2017

Theory of hybrid state in a metal with a small Fermi surface and strong collective excitations journal, May 2005

One-Dimensional Spin-Liquid without Magnon Excitations journal, May 1997

Properties of the chiral spin liquid state in generalized spin ladders journal, July 1997

A theory of 2+1D bosonic topological orders journal, November 2015

Fractional Quantum Hall Effect in an Array of Quantum Wires journal, January 2002

Crossed sliding Luttinger liquid phase journal, February 2001

Wire deconstructionism of two-dimensional topological phases journal, November 2014

Effects of interactions on the topological classification of free fermion systems journal, April 2010

Topological Orders and Chern-Simons Theory in Strongly Correlated Quantum Liquid journal, June 1991

Pairing in Luttinger Liquids and Quantum Hall States journal, July 2017

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model text, January 2001

Quantum Field Theory in Condensed Matter Physics journal, February 1997

From Luttinger liquid to non-Abelian quantum Hall states text, January 2011

Interaction effect on topological classification of superconductors in two dimensions text, January 2012

Chiral Spin Liquids in Arrays of Spin Chains text, January 2015

A theory of 2+1D bosonic topological orders text, January 2015

Pairing in Luttinger Liquids and Quantum Hall States text, January 2017

Anyons in an exactly solved model and beyond text, January 2005

Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains text, January 1995

The Non Linear Sigma Model and Spin Ladders text, January 1995

One-dimensional spin-liquid without magnon excitations text, January 1996

Correlation Lengths in Quantum Spin Ladders text, January 1997

Properties of the chiral spin liquid state in generalized spin ladders text, January 1997

Exact solution of an integrable anisotropic $\boldsymbol{J_1-J_2}$ spin chain model journal, January 2020

Model of spin liquids with and without time-reversal symmetry journal, May 2019

From coupled wires to coupled layers: Model with three-dimensional fractional excitations journal, June 2019

Ground-state degeneracy of non-Abelian topological phases from coupled wires journal, June 2019

Coupled-wire constructions: a Luttinger liquid approach to topology journal, February 2020

Ground-state degeneracy of non-Abelian topological phases from coupled wires text, January 2019

Model of spin liquids with and without time-reversal symmetry text, January 2018

Coupled-wire constructions: a Luttinger liquid approach to topology text, January 2019

Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
journal, October 2010

Fate of spinons in spontaneously dimerized spin- $\frac{1}{2}$ ladders
journal, April 2000

Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
journal, May 2016

Interaction effect on topological classification of superconductors in two dimensions
journal, August 2013

Anyons in an exactly solved model and beyond
journal, January 2006

Weakly coupled one-dimensional Mott insulators
journal, March 2002

The nonlinear sigma model and spin ladders
journal, June 1996

Form factors of soliton-creating operators in the sine-Gordon model
journal, July 2001

From Luttinger liquid to non-Abelian quantum Hall states
journal, February 2014

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model
journal, February 2001

Some properties of the model in two dimensions
journal, September 1978

The S-matrix of the kinks of the model
journal, September 1978

Correlation Lengths in Quantum Spin Ladders
journal, May 1997

Theory of (2+1)-dimensional fermionic topological orders and fermionic/bosonic topological orders with symmetries
journal, October 2016

Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains
journal, April 1996

Chiral spin liquids in arrays of spin chains
journal, June 2015

Detecting Topological Order in a Ground State Wave Function
journal, March 2006

Dimensional Crossover in Quantum Antiferromagnets
journal, November 1996

Topological Entanglement Entropy
journal, March 2006

Coupled spin- $\frac{1}{2}$ ladders as microscopic models for non-Abelian chiral spin liquids
journal, April 2017

Theory of hybrid state in a metal with a small Fermi surface and strong collective excitations
journal, May 2005

One-Dimensional Spin-Liquid without Magnon Excitations
journal, May 1997

Properties of the chiral spin liquid state in generalized spin ladders
journal, July 1997

A theory of 2+1D bosonic topological orders
journal, November 2015

Fractional Quantum Hall Effect in an Array of Quantum Wires
journal, January 2002

Crossed sliding Luttinger liquid phase
journal, February 2001

Wire deconstructionism of two-dimensional topological phases
journal, November 2014

Effects of interactions on the topological classification of free fermion systems
journal, April 2010

Topological Orders and Chern-Simons Theory in Strongly Correlated Quantum Liquid
journal, June 1991

Pairing in Luttinger Liquids and Quantum Hall States
journal, July 2017

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model
text, January 2001

Quantum Field Theory in Condensed Matter Physics
journal, February 1997

From Luttinger liquid to non-Abelian quantum Hall states
text, January 2011

Interaction effect on topological classification of superconductors in two dimensions
text, January 2012

Chiral Spin Liquids in Arrays of Spin Chains
text, January 2015

A theory of 2+1D bosonic topological orders
text, January 2015

Pairing in Luttinger Liquids and Quantum Hall States
text, January 2017

Anyons in an exactly solved model and beyond
text, January 2005

Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
text, January 1995

The Non Linear Sigma Model and Spin Ladders
text, January 1995

One-dimensional spin-liquid without magnon excitations
text, January 1996

Correlation Lengths in Quantum Spin Ladders
text, January 1997

Properties of the chiral spin liquid state in generalized spin ladders
text, January 1997

Exact solution of an integrable anisotropic $\boldsymbol{J_1-J_2}$ spin chain model
journal, January 2020

Model of spin liquids with and without time-reversal symmetry
journal, May 2019

From coupled wires to coupled layers: Model with three-dimensional fractional excitations
journal, June 2019

Ground-state degeneracy of non-Abelian topological phases from coupled wires
journal, June 2019

Coupled-wire constructions: a Luttinger liquid approach to topology
journal, February 2020

Ground-state degeneracy of non-Abelian topological phases from coupled wires
text, January 2019

Model of spin liquids with and without time-reversal symmetry
text, January 2018

Coupled-wire constructions: a Luttinger liquid approach to topology
text, January 2019