Chiral spin liquid with spinon Fermi surfaces in the spin-$\frac{1}{2}$ triangular Heisenberg model

Gong, Shou-Shu; Zheng, Wayne; Lee, Mac; Lu, Yuan-Ming; Sheng, D. N.

doi:10.1103/physrevb.100.241111

Title: Chiral spin liquid with spinon Fermi surfaces in the spin-$$\frac{1}{2}$$ triangular Heisenberg model

Abstract

Here, we study the interplay of competing interactions in spin-$$\frac{1}{2}$$ triangular Heisenberg model through tuning the first- ($$J_1$$), second- ($$J_2$$), and third-neighbor ($$J_ 3$$) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate $$J_2$$ and $$J_ 3$$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the U(1) staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the U(1) Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero $$J_2$$ and $$J_3$$, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.

Authors:

^[1]; Zheng, Wayne ^[2]; Lee, Mac ^[3]; Lu, Yuan-Ming ^[2]; Sheng, D. N. ^[4]

Beihang University, Beijing (China)
The Ohio State Univ., Columbus, OH (United States)
California State Univ., Northridge, CA (United States); Univ. of California, San Diego, CA (United States)
California State Univ., Northridge, CA (United States)

Publication Date:: Mon Dec 16 00:00:00 EST 2019

Research Org.:: California State Univ. (CalState), Long Beach, CA (United States)

Sponsoring Org.:: National Natural Science Foundation of China (NSFC); Fundamental Research Funds for the Central Universities; National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1800369

Grant/Contract Number:: FG02-06ER46305; 11874078; 11834014; DMR-1828019; DMR-1653769

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. B

Additional Journal Information:: Journal Volume: 100; Journal Issue: 24; 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; Materials Science; Physics

Citation Formats


                    Gong, Shou-Shu, Zheng, Wayne, Lee, Mac, Lu, Yuan-Ming, and Sheng, D. N. Chiral spin liquid with spinon Fermi surfaces in the spin-$\frac{1}{2}$ triangular Heisenberg model.  United States: N. p., 2019. 
Web.  doi:10.1103/physrevb.100.241111.

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                    Gong, Shou-Shu, Zheng, Wayne, Lee, Mac, Lu, Yuan-Ming, & Sheng, D. N. Chiral spin liquid with spinon Fermi surfaces in the spin-$\frac{1}{2}$ triangular Heisenberg model.  United States.  https://doi.org/10.1103/physrevb.100.241111

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                    Gong, Shou-Shu, Zheng, Wayne, Lee, Mac, Lu, Yuan-Ming, and Sheng, D. N. Mon .  
"Chiral spin liquid with spinon Fermi surfaces in the spin-$\frac{1}{2}$ triangular Heisenberg model".  United States.  https://doi.org/10.1103/physrevb.100.241111.  https://www.osti.gov/servlets/purl/1800369.

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@article{osti_1800369,

  title        = {Chiral spin liquid with spinon Fermi surfaces in the spin-$\frac{1}{2}$ triangular Heisenberg model},

  author       = {Gong, Shou-Shu and Zheng, Wayne and Lee, Mac and Lu, Yuan-Ming and Sheng, D. N.},

  abstractNote = {Here, we study the interplay of competing interactions in spin-$\frac{1}{2}$ triangular Heisenberg model through tuning the first- ($J_1$), second- ($J_2$), and third-neighbor ($J_ 3$) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate $J_2$ and $J_ 3$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the U(1) staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the U(1) Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero $J_2$ and $J_3$, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.},

  doi          = {10.1103/physrevb.100.241111},

  journal      = {Physical Review. B},

  number       = 24,

  volume       = 100,

  place        = {United States},

  year         = {Mon Dec 16 00:00:00 EST 2019},

  month        = {Mon Dec 16 00:00:00 EST 2019}

}

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Title: Chiral spin liquid with spinon Fermi surfaces in the spin-$$\frac{1}{2}$$ triangular Heisenberg model

Abstract

Citation Formats

The non-Abelian density matrix renormalization group algorithm journal, March 2002

Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model journal, September 2014

Thermodynamic properties of a spin-1/2 spin-liquid state in a κ-type organic salt journal, April 2008

Spinon Fermi surface U ( 1 ) spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator YbMgGaO 4 journal, August 2017

Quasiclassical magnetic order and its loss in a spin- 1 2 Heisenberg antiferromagnet on a triangular lattice with competing bonds journal, January 2015

Magnetic Interactions in the Geometrically Frustrated Triangular Lattice Antiferromagnet CuFeO 2 journal, October 2007

Quantum spin liquids: a review journal, November 2016

Quantum orders and symmetric spin liquids journal, April 2002

Competing spin-liquid states in the spin- 1 2 Heisenberg model on the triangular lattice journal, October 2015

Chiral Spin Liquid in a Frustrated Anisotropic Kagome Heisenberg Model journal, April 2014

Thermal-transport measurements in a quantum spin-liquid state of the frustrated triangular magnet κ-(BEDT-TTF)2Cu2(CN)3 journal, November 2008

Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet journal, April 2011

Quantum spin liquid states journal, April 2017

Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States journal, July 2008

Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model text, January 2013

Spiral phases in easy plane J1-J2-J3 triangular antiferromagnets journal, February 1995

A new high-temperature quantum spin liquid with polaron spins text, January 2017

A Quantum Dipolar Spin Liquid text, January 2015

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

Spin Bose-metal phase in a spin- 1 2 model with ring exchange on a two-leg triangular strip journal, May 2009

Projective symmetry group classification of chiral spin liquids text, January 2015

Fractionalization in the cuprates: Detecting the topological order text, January 2000

A quantum dipolar spin liquid journal, February 2018

Spin liquid nature in the Heisenberg J 1 − J 2 triangular antiferromagnet journal, April 2016

Large- N expansion for frustrated quantum antiferromagnets journal, April 1991

Neutron powder diffraction study of the two-dimensional triangular lattice antiferromagnet CuCrO 2 journal, May 1990

Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice text, January 1998

Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons journal, June 1992

1T-TaS 2 as a quantum spin liquid journal, June 2017

Unifying description of competing orders in two-dimensional quantum magnets journal, September 2019

Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice text, January 2017

Z 2 gauge theory of electron fractionalization in strongly correlated systems journal, September 2000

Inversion-symmetry breaking in the noncollinear magnetic phase of the triangular-lattice antiferromagnet Cu Fe O 2 journal, June 2006

Projective symmetry group classification of chiral spin liquids journal, March 2016

Dirac Spin Liquid on the Spin- 1 / 2 Triangular Heisenberg Antiferromagnet journal, November 2019

Quantum Spin Liquid States text, January 2016

Kapellasite: A Kagome Quantum Spin Liquid with Competing Interactions journal, July 2012

Unifying Description of Competing Orders in Two Dimensional Quantum Magnets text, January 2018

Spin liquids in frustrated magnets journal, March 2010

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

Topography of Spin Liquids on a Triangular Lattice journal, May 2018

Gapless excitations in the ground state of 1 T − TaS 2 journal, November 2017

Magnetic Interaction in the Geometrically Frustrated Triangular Lattice Antiferromagnet $\rm CuFeO_2$ text, January 2007

The Non-Abelian Density Matrix Renormalization Group Algorithm text, January 2000

Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4 journal, October 2018

Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model text, January 2014

Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections journal, March 2018

Variational study of triangular lattice spin- 1 ∕ 2 model with ring exchanges and spin liquid state in κ − ( ET ) 2 Cu 2 ( CN ) 3 journal, July 2005

Hierarchy of exchange interactions in the triangular-lattice spin-liquid YbMgGaO$_{4}$ text, January 2017

The half-filled Landau level: The case for Dirac composite fermions journal, April 2016

Mean-field theory of spin-liquid states with finite energy gap and topological orders journal, August 1991

The half-filled Landau level: the case for Dirac composite fermions text, January 2015

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice journal, August 2016

Highly Mobile Gapless Excitations in a Two-Dimensional Candidate Quantum Spin Liquid journal, June 2010

Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice journal, February 2015

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4 journal, December 2016

Rare-Earth Triangular Lattice Spin Liquid: A Single-Crystal Study of YbMgGaO 4 journal, October 2015

Spin liquid phase of the S = 1 2 J 1 − J 2 Heisenberg model on the triangular lattice journal, July 2015

Normal-state properties of the uniform resonating-valence-bond state journal, May 1990

Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor κ − ( ET ) 2 Cu 2 ( CN ) 3 journal, October 2005

Symmetry fractionalization in the topological phase of the spin- 1 2 J 1 − J 2 triangular Heisenberg model journal, September 2016

Fractionalization in the Cuprates: Detecting the Topological Order text, January 2001

Gauge theory of the normal state of high- T c superconductors journal, September 1992

Heat transport study of the spin liquid candidate 1 T − TaS 2 journal, August 2017

Investigation of the chiral antiferromagnetic Heisenberg model using projected entangled pair states journal, September 2017

Resonating valence bonds: A new kind of insulator? journal, February 1973

Gapless fermions and gauge fields in dielectrics journal, May 1989

Symmetric Z 2 spin liquids and their neighboring phases on triangular lattice journal, April 2016

Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice journal, July 1999

Spinon Fermi Surface in a Cluster Mott Insulator Model on a Triangular Lattice and Possible Application to 1 T − Ta S 2 journal, July 2018

Entanglement entropy and quantum field theory journal, June 2004

Doping a Mott insulator: Physics of high-temperature superconductivity journal, January 2006

Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension journal, November 2015

Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4 journal, July 2018

Spin Bose-Metal and Valence Bond Solid Phases in a Spin- 1 / 2 Model with Ring Exchanges on a Four-Leg Triangular Ladder journal, April 2011

Fractionalization in the Cuprates: Detecting the Topological Order journal, January 2001

A high-temperature quantum spin liquid with polaron spins journal, July 2017

The non-Abelian density matrix renormalization group algorithm
journal, March 2002

Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
journal, September 2014

Thermodynamic properties of a spin-1/2 spin-liquid state in a κ-type organic salt
journal, April 2008

Spinon Fermi surface $U (1)$ spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator ${YbMgGaO}_{4}$
journal, August 2017

Quasiclassical magnetic order and its loss in a spin- $\frac{1}{2}$ Heisenberg antiferromagnet on a triangular lattice with competing bonds
journal, January 2015

Magnetic Interactions in the Geometrically Frustrated Triangular Lattice Antiferromagnet ${CuFeO}_{2}$
journal, October 2007

Quantum spin liquids: a review
journal, November 2016

Quantum orders and symmetric spin liquids
journal, April 2002

Competing spin-liquid states in the spin- $\frac{1}{2}$ Heisenberg model on the triangular lattice
journal, October 2015

Chiral Spin Liquid in a Frustrated Anisotropic Kagome Heisenberg Model
journal, April 2014

Thermal-transport measurements in a quantum spin-liquid state of the frustrated triangular magnet κ-(BEDT-TTF)2Cu2(CN)3
journal, November 2008

Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet
journal, April 2011

Quantum spin liquid states
journal, April 2017

Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
journal, July 2008

Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
text, January 2013

Spiral phases in easy plane J1-J2-J3 triangular antiferromagnets
journal, February 1995

A new high-temperature quantum spin liquid with polaron spins
text, January 2017

A Quantum Dipolar Spin Liquid
text, January 2015

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

Spin Bose-metal phase in a spin- $\frac{1}{2}$ model with ring exchange on a two-leg triangular strip
journal, May 2009

Projective symmetry group classification of chiral spin liquids
text, January 2015

Fractionalization in the cuprates: Detecting the topological order
text, January 2000

A quantum dipolar spin liquid
journal, February 2018

Spin liquid nature in the Heisenberg $J_{1} - J_{2}$ triangular antiferromagnet
journal, April 2016

Large- N expansion for frustrated quantum antiferromagnets
journal, April 1991

Neutron powder diffraction study of the two-dimensional triangular lattice antiferromagnet CuCrO ₂
journal, May 1990

Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice
text, January 1998

Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons
journal, June 1992

1T-TaS ₂ as a quantum spin liquid
journal, June 2017

Unifying description of competing orders in two-dimensional quantum magnets
journal, September 2019

Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice
text, January 2017

$Z_{2}$ gauge theory of electron fractionalization in strongly correlated systems
journal, September 2000

Inversion-symmetry breaking in the noncollinear magnetic phase of the triangular-lattice antiferromagnet $Cu Fe O_{2}$
journal, June 2006

Projective symmetry group classification of chiral spin liquids
journal, March 2016

Dirac Spin Liquid on the Spin- $1 / 2$ Triangular Heisenberg Antiferromagnet
journal, November 2019

Quantum Spin Liquid States
text, January 2016

Kapellasite: A Kagome Quantum Spin Liquid with Competing Interactions
journal, July 2012

Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
text, January 2018

Spin liquids in frustrated magnets
journal, March 2010

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

Topography of Spin Liquids on a Triangular Lattice
journal, May 2018

Gapless excitations in the ground state of $1 T − {TaS}_{2}$
journal, November 2017

Magnetic Interaction in the Geometrically Frustrated Triangular Lattice Antiferromagnet $\rm CuFeO_2$
text, January 2007

The Non-Abelian Density Matrix Renormalization Group Algorithm
text, January 2000

Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4
journal, October 2018

Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model
text, January 2014

Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections
journal, March 2018

Variational study of triangular lattice spin- $1 ∕ 2$ model with ring exchanges and spin liquid state in $κ − {(ET)}_{2} {Cu}_{2} {(CN)}_{3}$
journal, July 2005

Hierarchy of exchange interactions in the triangular-lattice spin-liquid YbMgGaO$_{4}$
text, January 2017

The half-filled Landau level: The case for Dirac composite fermions
journal, April 2016

Mean-field theory of spin-liquid states with finite energy gap and topological orders
journal, August 1991

The half-filled Landau level: the case for Dirac composite fermions
text, January 2015

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice
journal, August 2016

Highly Mobile Gapless Excitations in a Two-Dimensional Candidate Quantum Spin Liquid
journal, June 2010

Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice
journal, February 2015

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
journal, December 2016

Rare-Earth Triangular Lattice Spin Liquid: A Single-Crystal Study of ${YbMgGaO}_{4}$
journal, October 2015

Spin liquid phase of the $S = \frac{1}{2} J_{1} - J_{2}$ Heisenberg model on the triangular lattice
journal, July 2015

Normal-state properties of the uniform resonating-valence-bond state
journal, May 1990

Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor $κ − (ET)_{2} {Cu}_{2} (CN)_{3}$
journal, October 2005

Symmetry fractionalization in the topological phase of the spin- $\frac{1}{2}$ $J_{1} − J_{2}$ triangular Heisenberg model
journal, September 2016

Fractionalization in the Cuprates: Detecting the Topological Order
text, January 2001

Gauge theory of the normal state of high- $T_{c}$ superconductors
journal, September 1992

Heat transport study of the spin liquid candidate $1 T − {TaS}_{2}$
journal, August 2017

Investigation of the chiral antiferromagnetic Heisenberg model using projected entangled pair states
journal, September 2017

Resonating valence bonds: A new kind of insulator?
journal, February 1973

Gapless fermions and gauge fields in dielectrics
journal, May 1989

Symmetric $Z_{2}$ spin liquids and their neighboring phases on triangular lattice
journal, April 2016

Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice
journal, July 1999

Spinon Fermi Surface in a Cluster Mott Insulator Model on a Triangular Lattice and Possible Application to $1 T − {Ta S}_{2}$
journal, July 2018

Entanglement entropy and quantum field theory
journal, June 2004

Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006

Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
journal, November 2015

Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid ${YbMgGaO}_{4}$
journal, July 2018

Spin Bose-Metal and Valence Bond Solid Phases in a Spin- $1 / 2$ Model with Ring Exchanges on a Four-Leg Triangular Ladder
journal, April 2011

Fractionalization in the Cuprates: Detecting the Topological Order
journal, January 2001

A high-temperature quantum spin liquid with polaron spins
journal, July 2017

Spin-Driven Ferroelectricity in Triangular Lattice Antiferromagnets $A {CrO}_{2}$ ( $A = Cu$ , Ag, Li, or Na)
journal, August 2008

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
text, January 2016

Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice
journal, January 2018