Su-Peng Kou ()Beijing Normal University
OutlineMotivationTopological spin density waves in correlated topological insulatorsQuantum spin liquid states in correlated topological insulatorsConclusion Kou SPPHYS. REV. B 78, 2331042008.  Sun GY and Kou SP, EPL, 87 67002 (2009). Kou SP, and Liu LFEUR. PHYS. J. B. 81, 165 (2011) .  Sun GY and Kou SP, J. Phys. C 23 (2011) 045603.  He J, Kou SP, Liang Y, Feng SP, PHYS. REV. B 83, 205116 (2011) . He J, Zong YH, Kou SP, Liang Y, Feng SP, PHYS. REV. B 84, 035127 (2011) . He J, Liang Y, Kou SP, PHYS. REV. B. 85, 205107 (2012). He J, Wang B, Kou SP, PHYS. REV. B. submitted, arXiv:1204.4766. Kou SP, Insulators: Types, Properties and Uses (Nova Science Publishers).
I. Motivation: Look for quantum exotic states in correlated topological insulatorX. G. Wen, Quantum Field Theory of Many-Body Systems
Spin liquid emergent in physicsNo broken symmetryDeconfined spinons+Spin liquidEmergent gauge field+
Spin orders in strongly correlated electron systems G. Misguich, arXiv:cond-mat/0310405
II. Topological spin density wave states in correlated topological insulatorsInstability of an interacting fermion system with topologically nontrivial band structureInteracting spinful Haldane modelInteracting Kane-Mele model
The spinful Haldane model spin rotation symmetry, no T symmetry
The Kane-Mele model T symmetry, no spin rotation symmetry Kane and Mele, Phys. Rev. Lett. 95, 146802 (2005) http://www.physics.upenn.edu/~kane/
Possible quantum spin liquid in the interacting Kane-Mele model T symmetry, no spin rotation symmetry Slave-rotor theory: Stephan Rachel and Karyn Le Hury, Phys. Rev. B 82. 075106 (2010)QMC: M. Hohenadler, T. C. Lang, F. F. Assaad, Phys. Rev. Lett. 106, 100403 (2011) Dong Zheng, Congjun Wu and Guang-Ming Zhang, Phys. Rev. B 84, 205121 (2011) VCA : Shun-Li Yu, X.C. Xie, Jian-Xin Li, Phys. Rev. Lett. 107, 010401 (2011) DMF: Wei Wu, S. Rachel, Wu-Ming Liu, K. Le Hur, Phys. Rev. B 85, 205102 (2012)
1. Topological spin-density-wave states in interacting spinful Haldane model - spin rotation symmetry, no T symmetry He J, Zong YH, Kou SP, Liang Y, Feng SP, PHYS. REV. B 84, 035127 (2011)What is the ground state for the spinful Haldane model with the on-site interaction?
Mean field equationwhereMean field approachM is the staggered magnetization.
Phase diagramC=2 topological insulator - QAHBand insulatorTrivial AF-SDW orderB-type topologicalSDW orderA-type topologicalSDW order
Low energy effective model
Spin-charge separated charge-flux binding effect in A-TSDW
spin-charge synchronization charge-flux binding effect in B-TSDW
Different spin-density-wave states in correlated topological insulators with the same local order parameter may have different topological properties, including the induced quantum numbers on topological objects, the edge states, the quantum Hall effects.
2. Quantum spin orders in correlated topological insulator with flat-band
Possible fractional quanum hall states
What is the ground state for the correlated topological insulators in the flat-band limit?Whats the dispersion of electrons and spin waves for correlated topological insulators in the flat-band limit?
Phase diagram : electrons on TFBd is the hole concentration.FM (topological) spin-density-wave
Dispersion of electrons in A-TSDWDispersion of spin-waves in A-TSDWA-TSDW : Half filling caseA-TSDWAF-SDWTFBTFB
FM (topological) spin-density-wave: quarter filling caseDispersion of electrons in FM order Dispersion of spin wave in FM order
FM order and AF order :d=0.3 filling caseDispersion of electronsOrder parameters
III. Quantum spin liquids in interacting spinful Haldane modelShort range A-type topological spin density wave state: chiral spin liquidShort range B-type topological spin density wave state : composite spin liquid
Quantum spin-fluctuations in topological spin density wave statesTransverse spin susceptibility isSpin coupling constantSpin wave velocityX. G. Wen, Quantum Field Theory of Many-Body Systems,(Oxford Univ. Press, Oxford, 2004)One obtains spin stiffness and the transverse spin susceptibility: H.J. Schulz, in The hubbard Model, edited by D. Baeriswyl(Plenum, New York, 1995).Z. Y. Weng, C. S. Ting, and T. K. Lee, Phys. Rev. B43, 3790 (1991).K. Borejsza, N. Dupuis, Euro Phys. Lett. 63, 722 (2003); Phys. Rev. B 69, 085119 (2004).
Spin coupling constant t=0.0228tt=0.1t
What is the nature of the quantum disordered states for TSDWs? S. Chakravarty, et al., Phys. Rev. B 39, 2344 (1989).
He J, Liang Y, Kou SP, PHYS. REV. B. 85, 205107 (2012).
Properties of chiral spin liquidSpinon is semion with fractional statisticsGround state degeneracy : 2 on torusChiral gapless edge states He J, Liang Y, Kou SP, PHYS. REV. B. 85, 205107 (2012).X. G.Wen, F.Wilczek, and A. Zee, Phys. Rev. B 39, 11413 (1989).
Mean field approach
C=2 topological insulatorChiral spin liquidTrvial AF orderA-TSDW
Chiral spin order parameter
- vortex is semion Statistics angle = /2 With induced fermion number , -vortex becomes semion.
Effective Lagrangian from slave-rotor approach N = 4
?S=1/2, charge e fermion
Composite spin liquidspin liquid
g > gcg < gcS=1/2, charge e fermion?
To be confirmed by QMC, ?
Thanks for your attention!
Spin susceptility of spin order in metallic spin order
1. Spin liquid in the -flux Hubbard model and the Hubbard model on honeycomb lattice
Quantum spin liquid near Mott transition of -flux Hubbard modelSun GY and Kou SP, EPL, 87 67002 (2009).Kou SP, Liu LF, He J, Wu YJEUR. PHYS. J. B. 81, 165 (2011).
Gapless Z2 topological spin liquid There are three types of quasi-particles : gapped fermionic spinons, gapped bosonic spinons and the gapped gauge field.
Nodal spin liquidThere are three types of quasi-particles : gapless fermionic spinons, gapped bosonic spinons and the roton-like gauge field.
Results from QMCChia-Chen Chang and Richard T. Scalettar, Phys. Rev. Lett. 109, 026404 (2012)
Global Phase diagram by spin-fluctuation theorySun GY and Kou SP, J. Phys. C. 23 (2011) 045603
Quantum spin liquid from QMCZ. Y. Meng, T. C. Lang, S. Wessel, F. F. Assaad & A. Muramatsu, Nature 464, 847 (2010)
Results of the Hubbard Model on the Honeycomb Lattice from QMC of bigger sizeSandro Sorella, Yuichi Otsuka, Seiji Yunoki, arXiv:1207.1783.
*This is my outline. First Ill talk our motivation; then I discuss the topological spin-density-wave states in correlated topological insulators; next we point out that there may exist quantum spin liquid states in this system. Finally I give the conclusion.**In a correlated electron system, the spin liquid state can be a ground state which has no symmetry breaking, but has deconfined spinons, and the emergent gauge field*In the intermediate coupling region, there may exist new types of quantum states. The fermions with topologically nontrivial band structure**Because this is a bipartite model, we may consider the antiferromagnetic order**When we integrate the gapped fermion fields, we derive the effective Chern-Simons-Hopf term of the gauge fields*The skyrmion is really a charged fermionic excitation.**The green plane denotes the position of the chemical potential; the read plane and the blue plane are the flat band. The spin wave's dispersion of this FM order shows quadratic behavior.**The chiral spin order parameter is a property of the chiral spin liquid.*