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Volumn 112, Issue 13, 2014, Pages

Chiral spin liquid in a frustrated anisotropic kagome heisenberg model

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; QUANTUM ENTANGLEMENT; STATISTICAL MECHANICS; SUPERCONDUCTING MATERIALS; SUPERCONDUCTIVITY; TOPOLOGY;

EID: 84898481524     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.137202     Document Type: Article
Times cited : (261)

References (52)
  • 1
    • 0000145935 scopus 로고
    • IJPBEV 0217-9792 10.1142/S0217979290000139
    • X.-G. Wen, Int. J. Mod. Phys. B 04, 239 (1990). IJPBEV 0217-9792 10.1142/S0217979290000139
    • (1990) Int. J. Mod. Phys. B , vol.4 , pp. 239
    • Wen, X.-G.1
  • 2
    • 0015586907 scopus 로고
    • MRBUAC 0025-5408 10.1016/0025-5408(73)90167-0
    • P.W. Anderson, Mater. Res. Bull. 8, 153 (1973). MRBUAC 0025-5408 10.1016/0025-5408(73)90167-0
    • (1973) Mater. Res. Bull. , vol.8 , pp. 153
    • Anderson, P.W.1
  • 3
    • 77949366361 scopus 로고    scopus 로고
    • NATUAS 0028-0836 10.1038/nature08917
    • L. Balents, Nature (London) 464, 199 (2010). NATUAS 0028-0836 10.1038/nature08917
    • (2010) Nature (London) , vol.464 , pp. 199
    • Balents, L.1
  • 4
    • 4243642327 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.66.1773
    • N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991). PRLTAO 0031-9007 10.1103/PhysRevLett.66.1773
    • (1991) Phys. Rev. Lett. , vol.66 , pp. 1773
    • Read, N.1    Sachdev, S.2
  • 5
    • 3743130827 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.61.2376
    • D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.61.2376
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 2376
    • Rokhsar, D.S.1    Kivelson, S.A.2
  • 7
    • 17144436460 scopus 로고    scopus 로고
    • Resonating valence bond phase in the triangular lattice quantum dimer model
    • DOI 10.1103/PhysRevLett.86.1881
    • R. Moessner and S.L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.1881 (Pubitemid 32252800)
    • (2001) Physical Review Letters , vol.86 , Issue.9 , pp. 1881-1884
    • Moessner, R.1    Sondhi, S.L.2
  • 8
    • 0036612544 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.65.224412
    • L. Balents, M.P.A. Fisher, and S.M. Girvin, Phys. Rev. B 65, 224412 (2002). PRBMDO 0163-1829 10.1103/PhysRevB.65.224412
    • (2002) Phys. Rev. B , vol.65 , pp. 224412
    • Balents, L.1    Fisher, M.P.A.2    Girvin, S.M.3
  • 9
    • 0037268624 scopus 로고    scopus 로고
    • Fault-tolerant quantum computation by anyons
    • DOI 10.1016/S0003-4916(02)00018-0, PII S0003491602000180
    • A. Kitaev, Ann. Phys. (Amsterdam) 303, 2 (2003). APNYA6 0003-4916 10.1016/S0003-4916(02)00018-0 (Pubitemid 36177417)
    • (2003) Annals of Physics , vol.303 , Issue.1 , pp. 2-30
    • Kitaev, A.Yu.1
  • 11
    • 33947226050 scopus 로고    scopus 로고
    • Projected-wave-function study of the spin-1/2 heisenberg model on the kagomé lattice
    • DOI 10.1103/PhysRevLett.98.117205
    • Y. Ran, M. Hermele, P.A. Lee, and X.-G. Wen, Phys. Rev. Lett. 98, 117205 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.117205 (Pubitemid 46434373)
    • (2007) Physical Review Letters , vol.98 , Issue.11 , pp. 117205
    • Ran, Y.1    Hermele, M.2    Lee, P.A.3    Wen, X.-G.4
  • 12
    • 3543034352 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.59.2095
    • V. Kalmeyer and R.B. Laughlin, Phys. Rev. Lett. 59, 2095 (1987); PRLTAO 0031-9007 10.1103/PhysRevLett.59.2095
    • (1987) Phys. Rev. Lett. , vol.59 , pp. 2095
    • Kalmeyer, V.1    Laughlin, R.B.2
  • 13
    • 4243944879 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.39.11879
    • V. Kalmeyer and R.B. Laughlin, Phys. Rev. B 39, 11879 (1989). PRBMDO 0163-1829 10.1103/PhysRevB.39.11879
    • (1989) Phys. Rev. B , vol.39 , pp. 11879
    • Kalmeyer, V.1    Laughlin, R.B.2
  • 14
    • 37249040018 scopus 로고    scopus 로고
    • Exact chiral spin liquid with non-abelian anyons
    • DOI 10.1103/PhysRevLett.99.247203
    • H. Yao and S.A. Kivelson, Phys. Rev. Lett. 99, 247203 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.247203 (Pubitemid 350276635)
    • (2007) Physical Review Letters , vol.99 , Issue.24 , pp. 247203
    • Yao, H.1    Kivelson, S.A.2
  • 15
    • 84861557945 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.108.207204
    • L. Messio, B. Bernu, and C. Lhuillier, Phys. Rev. Lett. 108, 207204 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.207204
    • (2012) Phys. Rev. Lett. , vol.108 , pp. 207204
    • Messio, L.1    Bernu, B.2    Lhuillier, C.3
  • 16
    • 33751296541 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.60.2677
    • R.B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.60.2677
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 2677
    • Laughlin, R.B.1
  • 18
    • 35949009606 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.39.11413
    • X.-G. Wen, F. Wilczek, and A. Zee, Phys. Rev. B 39, 11413 (1989). PRBMDO 0163-1829 10.1103/PhysRevB.39.11413
    • (1989) Phys. Rev. B , vol.39 , pp. 11413
    • Wen, X.-G.1    Wilczek, F.2    Zee, A.3
  • 20
    • 0000110603 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.70.2641
    • K. Yang, L.K. Warman, and S.M. Girvin, Phys. Rev. Lett. 70, 2641 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.70.2641
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 2641
    • Yang, K.1    Warman, L.K.2    Girvin, S.M.3
  • 21
    • 0000092324 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.52.4223
    • F.D.M. Haldane and Daniel P. Arovas, Phys. Rev. B 52, 4223 (1995). PRBMDO 0163-1829 10.1103/PhysRevB.52.4223
    • (1995) Phys. Rev. B , vol.52 , pp. 4223
    • Haldane, F.D.M.1    Arovas, D.P.2
  • 22
    • 4043151514 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.64.1313
    • D.-H. Lee and C.L. Kane, Phys. Rev. Lett. 64, 1313 (1990). PRLTAO 0031-9007 10.1103/PhysRevLett.64.1313
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 1313
    • Lee, D.-H.1    Kane, C.L.2
  • 23
    • 4444247518 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.63.2524
    • G. Baskaran, Phys. Rev. Lett. 63, 2524 (1989). PRLTAO 0031-9007 10.1103/PhysRevLett.63.2524
    • (1989) Phys. Rev. Lett. , vol.63 , pp. 2524
    • Baskaran, G.1
  • 24
    • 0001141665 scopus 로고
    • JAPIAU 0021-8979 10.1063/1.347830
    • J. Marston and C. Zeng, J. Appl. Phys. 69, 5962 (1991). JAPIAU 0021-8979 10.1063/1.347830
    • (1991) J. Appl. Phys. , vol.69 , pp. 5962
    • Marston, J.1    Zeng, C.2
  • 26
    • 70349510889 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.103.135301
    • M. Hermele, V. Gurarie, and A.M. Rey, Phys. Rev. Lett. 103, 135301 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.135301
    • (2009) Phys. Rev. Lett. , vol.103 , pp. 135301
    • Hermele, M.1    Gurarie, V.2    Rey, A.M.3
  • 27
    • 34548404601 scopus 로고    scopus 로고
    • Spin hamiltonian for which the chiral spin liquid is the exact ground state
    • DOI 10.1103/PhysRevLett.99.097202
    • D.F. Schroeter, E. Kapit, R. Thomale, and M. Greiter, Phys. Rev. Lett. 99, 097202 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.99.097202 (Pubitemid 47357783)
    • (2007) Physical Review Letters , vol.99 , Issue.9 , pp. 097202
    • Schroeter, D.F.1    Kapit, E.2    Thomale, R.3    Greiter, M.4
  • 29
    • 84862528580 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.108.257206
    • A.E.B. Nielsen, J.I. Cirac, and G. Sierra, Phys. Rev. Lett. 108, 257206 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.257206
    • (2012) Phys. Rev. Lett. , vol.108 , pp. 257206
    • Nielsen, A.E.B.1    Cirac, J.I.2    Sierra, G.3
  • 31
    • 84898485158 scopus 로고    scopus 로고
    • arXiv:1307.8194.
    • M. Barkeshli, arXiv:1307.8194.
    • Barkeshli, M.1
  • 32
    • 3442895828 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.69.2863
    • S.R. White, Phys. Rev. Lett. 69, 2863 (1992); PRLTAO 0031-9007 10.1103/PhysRevLett.69.2863
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2863
    • White, S.R.1
  • 33
    • 20044389808 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.48.10345
    • S.R. White, Phys. Rev. B 48, 10345 (1993). PRBMDO 0163-1829 10.1103/PhysRevB.48.10345
    • (1993) Phys. Rev. B , vol.48 , pp. 10345
    • White, S.R.1
  • 34
    • 79957945867 scopus 로고    scopus 로고
    • SCIEAS 0036-8075 10.1126/science.1201080
    • S. Yan, D. Huse, and S.R. White, Science 332, 1173 (2011). SCIEAS 0036-8075 10.1126/science.1201080
    • (2011) Science , vol.332 , pp. 1173
    • Yan, S.1    Huse, D.2    White, S.R.3
  • 35
    • 51749102842 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.101.117203
    • H.-C. Jiang, Z.Y. Weng, and D.N. Sheng, Phys. Rev. Lett. 101, 117203 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.117203
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 117203
    • Jiang, H.-C.1    Weng, Z.Y.2    Sheng, D.N.3
  • 36
    • 84870609669 scopus 로고    scopus 로고
    • NPAHAX 1745-2473 10.1038/nphys2465
    • H.-C. Jiang, Z. Wang, and L. Balents, Nat. Phys. 8, 902 (2012). NPAHAX 1745-2473 10.1038/nphys2465
    • (2012) Nat. Phys. , vol.8 , pp. 902
    • Jiang, H.-C.1    Wang, Z.2    Balents, L.3
  • 38
    • 84897589613 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.89.075110
    • Y.-C. He, D.N. Sheng, and Y. Chen, Phys. Rev. B 89, 075110 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.075110
    • (2014) Phys. Rev. B , vol.89 , pp. 075110
    • He, Y.-C.1    Sheng, D.N.2    Chen, Y.3
  • 39
    • 84873457492 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.110.067208
    • L. Cincio and G. Vidal, Phys. Rev. Lett. 110, 067208 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.067208
    • (2013) Phys. Rev. Lett. , vol.110 , pp. 067208
    • Cincio, L.1    Vidal, G.2
  • 41
    • 84878697028 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.110.236801
    • M.P. Zaletel, R.S.K. Mong, and F. Pollmann, Phys. Rev. Lett. 110, 236801 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.236801
    • (2013) Phys. Rev. Lett. , vol.110 , pp. 236801
    • Zaletel, M.P.1    Mong, R.S.K.2    Pollmann, F.3
  • 42
    • 84898418975 scopus 로고    scopus 로고
    • See the Supplemental Material at for cylinder geometry of kagome lattice, numerical algorithm.
    • See the Supplemental Material at http://link.aps.org/supplemental/10. 1103/PhysRevLett.112.137202 for cylinder geometry of kagome lattice, numerical algorithm.
  • 44
    • 46949084674 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.101.010504
    • H. Li and F.D.M. Haldane, Phys. Rev. Lett. 101, 010504 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.010504
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 010504
    • Li, H.1    Haldane, F.D.M.2
  • 45
    • 33645151438 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.96.110404
    • A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.110404
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 110404
    • Kitaev, A.1    Preskill, J.2
  • 46
    • 33645161396 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.96.110405
    • M. Levin and X.-G. Wen, Phys. Rev. Lett. 96, 110405 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.110405
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 110405
    • Levin, M.1    Wen, X.-G.2
  • 47
    • 84898433509 scopus 로고    scopus 로고
    • Because of the difficulty of extrapolating the converged entanglement entropy for larger systems (YC12, XC12) and the finite size effect, the topological entanglement entropy (TEE) extrapolated from our data has a deviation from the theoretical value (Equation presented). However, a near accurate TEE term is obtained for the CSL in the SU2 model [46] by keeping around 16 000 states.
    • Because of the difficulty of extrapolating the converged entanglement entropy for larger systems (YC12, XC12) and the finite size effect, the topological entanglement entropy (TEE) extrapolated from our data has a deviation from the theoretical value (Equation presented). However, a near accurate TEE term is obtained for the CSL in the SU2 model [46] by keeping around 16 000 states.
  • 48
    • 36649005167 scopus 로고    scopus 로고
    • Variational quantum Monte Carlo simulations with tensor-network states
    • DOI 10.1103/PhysRevLett.99.220602
    • A.W. Sandvik and G. Vidal, Phys. Rev. Lett. 99, 220602 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.220602 (Pubitemid 350198451)
    • (2007) Physical Review Letters , vol.99 , Issue.22 , pp. 220602
    • Sandvik, A.W.1    Vidal, G.2
  • 50
  • 51
    • 84898409534 scopus 로고    scopus 로고
    • A state from a real-variable code is always time-reversal symmetric. The time-reversal invariant state here means a state with an exponentially decaying chiral correlation instead of a long-range chiral correlation as seen in Fig. 2.
    • A state from a real-variable code is always time-reversal symmetric. The time-reversal invariant state here means a state with an exponentially decaying chiral correlation instead of a long-range chiral correlation as seen in Fig. 2.


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