Symmetry protection of topological phases in one-dimensional quantum spin systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 85, Issue 7, 2012, Pages

  Pollmann, Frank ^a   Berg, Erez ^b   Turner, Ari M ^c   Oshikawa, Masaki ^d  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b HARVARD UNIVERSITY   (United States)

^c UNIVERSITY OF AMSTERDAM   (Netherlands)

^d UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84857749152     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.85.075125     Document Type: Article

References (39)

1. F. D. M. Haldane, Phys. Lett. 10.1016/0375-9601(83)90631-X 93A, 464 (1983).
2. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 50.1153 50, 1153 (1983).
3. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.799 59, 799 (1987).
4. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01218021 115, 477 (1988).
5. M. den Nijs and K. Rommelse, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.4709 40, 4709 (1989).
6. E. Berg, E. G. Dalla Torre, T. Giamarchi, and E. Altman, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.245119 77, 245119 (2008).
7. Z.-C. Gu and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.155131 80, 155131 (2009).
8. F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.064439 81, 064439 (2010).
9. A. M. Turner, F. Pollmann, and E. Berg, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.075102 83, 075102 (2011).
10. X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.035107 83, 035107 (2011).
11. X. Chen, Z.-C. Gu, and X.-G. Wen, e-print arXiv: 1103.3323.
12. N. Schuch, D. Pérez-García, and I. Cirac, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.165139 84, 165139 (2011).
13. M. Nakamura, E. J. Bergholtz, and J. Suorsa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.165102 81, 165102 (2010).
14. K. Hasebe and K. Totsuka, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.104426 84, 104426 (2011).
15. H.-C. Jiang, S. Rachel, Z.-Y. Weng, S.-C. Zhang, and Z. Wang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.220403 82, 220403 (2010).
16. T. Hirano, H. Katsura, and Y. Hatsugai, Phys. Rev. B 1098-0121 10.1103/PhysRevB.77.094431 77, 094431 (2008).
17. T. Kennedy, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/2/26/010 2, 5737 (1990).
18. T. Kennedy and H. Tasaki, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.45.304 45, 304 (1992).
19. M. Oshikawa, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/4/36/019 4, 7469 (1992).
20. K. Okunishi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.104411 83, 104411 (2011).
21. C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 95, 146802 (2005). (Pubitemid 41777602)
22. A. Kitazawa and K. Nomura, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.66.3944 66, 3944 (1997).
23. M. Fannes, B. Nachtergaele, and R. F. Werner, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02099178 144, 443 (1992).
24. A. Klümper, A. Schadschneider, and J. Zittartz, J. Phys. A: Math. Gen. JPHAC5 0305-4470 10.1088/0305-4470/24/16/012 24, L955 (1991).
25. D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum Inf. Comput. 7, 401 (2007).
26. G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.070201 98, 070201 (2007).
27. R. Orús and G. Vidal, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.155117 78, 155117 (2008).
28. D. Pérez-García, M. M. Wolf, M. Sanz, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.167202 100, 167202 (2008). (Pubitemid 351574581)
29. P. Calabrese and J. Cardy, J. Stat. Mech. 1742-5468 10.1088/1742-5468/ 2004/06/P06002 (2004) P06002.
30. M. M. Wolf, G. Ortiz, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.110403 97, 110403 (2006). (Pubitemid 44394855)
31. K. Totsuka and M. Suzuki, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/7/8/012 7, 1639 (1995).
32. E. Dagotto and T. M. Rice, Science SCIEAS 0036-8075 10.1126/science.271. 5249.618 271, 618 (1996).
33. Y. Nishiyama, N. Hatano, and M. Suzuki, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.64.1967 64, 1967 (1995).
34. S. Todo, M. Matsumoto, C. Yasuda, and H. Takayama, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.64.224412 64, 224412 (2001).
35. D. Poilblanc, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105. 077202 105, 077202 (2010).
36. A. M. Läuchli and J. Schliemann, Phys. Rev. B 1098-0121 10.1103/PhysRevB.85.054403 85, 054403 (2012).
37. D. Charrier, S. Capponi, M. Oshikawa, and P. Pujol, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.075108 82, 075108 (2010).
38. F. Anfuso and A. Rosch, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.085124 76, 085124 (2007).
39. T. Tonegawa, K. Okamoto, H. Nakano, T. Sakai, K. Nomura, and M. Kaburagi, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.80.043001 80, 043001 (2011).