Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains

Physical Review B - Condensed Matter and Materials Physics

Volumn 85, Issue 19, 2012, Pages

  Liu, Zheng Xin ^a   Zhou, Yi ^b   Tu, Hong Hao ^c   Wen, Xiao Gang ^a,d   Ng, Tai Kai ^e  

^a TSINGHUA UNIVERSITY   (China)

^b ZHEJIANG UNIVERSITY   (China)

^c MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^e HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84861682668     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.85.195144     Document Type: Article

References (70)

1. I. Affleck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54.966 54, 966 (1985);
2. I. Affleck and J. B. Marston, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.37.3774 37, 3774 (1988);
3. Daniel P. Arovas and Assa Auerbach, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.38.316 38, 316 (1988).
4. P. W. Anderson, Science SCIEAS 0036-8075 10.1126/science.235.4793.1196 235, 1196 (1987).
5. P. A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.78.17 78, 17 (2006). (Pubitemid 43279669)
6. Claudius Gros, Ann. Phys. APNYA6 0003-4916 10.1016/0003-4916(89)90077-8 189, 53 (1989).
7. W. Rantner and X.-G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3871 86, 3871 (2001); (Pubitemid 32425353)
8. M. Hermele, T. Senthil, M. P. A. Fisher, P. A. Lee, N. Nagaosa, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70.214437 70, 214437 (2004); (Pubitemid 40239483)
9. M. Hermele, T. Senthil, and M. P. A. Fisher, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.104404 72, 104404 (2005). (Pubitemid 43022367)
10. G. Baskaran, Z. Zou, and P. W. Anderson, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(87)90642-9 63, 973 (1987); (Pubitemid 18577690)
11. X. G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.44.2664 44, 2664 (1991);
12. O. I. Motrunich, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.045105 72, 045105 (2005); (Pubitemid 41526536)
13. Y. Ran, M. Hermele, P. A. Lee, and X.-G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.117205 98, 117205 (2007). (Pubitemid 46434373)
14. Z.-X. Liu, Y. Zhou, and T.-K. Ng, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.224417 81, 224417 (2010);
15. Z.-X. Liu, Y. Zhou, and T.-K. Ng, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.144422 82, 144422 (2010).
16. G. Fáth and J. Sólyom, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.44.11836 44, 11836 (1991);
17. G. Fáth and J. Sólyom, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.47.872 47, 872 (1993).
18. C. Itoi and M.-H. Kato, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.55.8295 55, 8295 (1997).
19. T. Murashima and K. Nomura, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.214431 73, 214431 (2006); (Pubitemid 43901026)
20. A. Läuchli, G. Schmid, and S. Trebst, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.144426 74, 144426 (2006). (Pubitemid 44656264)
21. F. D. M. Haldane, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(83) 90631-X 93, 464 (1983);
22. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 50.1153 50, 1153 (1983).
23. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.799 59, 799 (1987);
24. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01218021 115, 477 (1988).
25. A. Klümper, A. Schadschneider, and J. Zittartz, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/24/16/012 24, L955 (1991);
26. A. Klümper, A. Schadschneider, and J. Zittartz, Z. Phys. B ZPCMDN 0722-3277 10.1007/BF01309281 87, 281 (1992).
27. T. Kennedy and H. Tasaki, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.45.304 45, 304 (1992).
28. M. den Nijs and K. Rommelse, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.4709 40, 4709 (1989).
29. Z.-C. Gu and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.155131 80, 155131 (2009).
30. F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.064439 81, 064439 (2010).
31. X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.155138 82, 155138 (2010);
32. X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.035107 83, 035107 (2011).
33. Z.-X. Liu, M. Liu, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.075135 84, 075135 (2011);
34. Z.-X. Liu, M. Liu, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.195145 84, 195145 (2011).
35. X. Chen, Z.-X. Liu, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.235141 84, 235141 (2011);
36. X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, arXiv: 1106.4772.
37. I. Affleck, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(86)90167-7 265, 409 (1986);
38. I. Affleck, Nucl. Phys. B 10.1016/0550-3213(88)90117-4 305, 582 (1988).
39. A. Kitaev, Phys. Usp. PHUSEY 1063-7869 10.1070/1063-7869/44/10S/S29 44, 131 (2001);
40. L. Fidkowski and A. Kitaev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.075103 83, 075103 (2011).
41. N. Read and D. Green, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.61. 10267 61, 10267 (2000).
42. Z. X. Liu (unpublished).
43. We have set the dimension of the matrices (or the number of Schmit eigenvalues) as 48. The algorithm is following G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.070201 98, 070201 (2007).
44. S. R. White and D. A. Huse, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.48.3844 48, 3844 (1993).
45. S. Qin, T. K. Ng, and Z.-B. Su, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.52.12844 52, 12844 (1995).
46. K. Nomura, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.2421 40, 2421 (1989).
47. L. A. Takhatajan, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(82) 90764-2 87, 479 (1982);
48. H. M. Babujian, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(82) 90403-0 90, 479 (1982).
49. H.-H. Tu, G.-M. Zhang, and T. Xiang, J. Phys. A 1751-8113 10.1088/1751-8113/41/41/415201 41, 415201 (2008);
50. H.-H. Tu, G.-M. Zhang, and T. Xiang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.094404 78, 094404 (2008);
51. H.-H. Tu, G.-M. Zhang, T. Xiang, Z.-X. Liu, and T.-K. Ng, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.014401 80, 014401 (2009).
52. 2 instanton has a finite action and a finite density. Consequently, the ground state of the weak pairing phase is doubly degenerate and dimerized. The weak pairing and strong pairing phases can still be distinguished by their different topology. The analysis from mean-field theory also agrees with the Majorana effective field theory in Ref..
53. H.-H. Tu and R. Orus, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.077204 107, 077204 (2011).
54. X. G. Wen, Quantum Field Theory of Many-body Systems (Oxford University Press, 2004).
55. P. Lecheminant and E. Orignac, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.174406 65, 174406 (2002).
56. A. M. Tsvelik, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.42.10499 42, 10499 (1990).
57. H. Tsunetsugu and M. Arikawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.75.083701 75, 083701 (2006).
58. G. V. Uimin, JETP Letters 12, 225 (1970);
59. C. K. Lai, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1666522 15, 1675 (1974);
60. B. Sutherland, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.12.3795 12, 3795 (1975).
61. N. Kawakami, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.46.3191 46, 3191 (1992).
62. T. K. Ng, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.45.8181 45, 8181 (1992);
63. T. K. Ng, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.47.11575 47, 11575 (1993);
64. T. K. Ng, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.50.555 50, 555 (1994).
65. J. B. Parkinson, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/20/36/011 20, L1029 (1987);
66. M. N. Barber and M. T. Batchelor, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.4621 40, 4621 (1989).
67. A. E. B. Nielsen, J. I. Cirac, and G. Sierra, J. Stat. Mech. 1742-5468 10.1088/1742-5468/2011/11/P11014 (2011) P11014.
68. R. Thomale, S. Rachel, P. Schmitteckert, and M. Greiter, arXiv: 1110.5956;
69. M. Greiter, J. Low Temp. Phys. JLTPAC 0022-2291 10.1023/A:1013807011292 126, 1029 (2002); (Pubitemid 34409487)
70. Mapping of Parent Hamiltonians, Springer Tracts of Modern Physics (Springer, Berlin, 2011).