2009

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

Pollmann, Frank, Berg, Erez, Turner, Ari M. et al.

Understand

We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments.

We find that an odd-$S$ Haldane phase is a topologically non-trivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of $\pi$-rotations about $x,y$ and $z$ axes; (ii) time-reversal symmetry $S^{x,y,z} \rightarrow - S^{x,y,z}$; (iii) link inversion symmetry (reflection about a bond center), consistently with previous results [Phys.
Rev.
B \textbf{81}, 064439 (2010)].

I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. 115
1988
Earlier work this paper cites.
M. den Nijs and K. Rommelse, Phys. Rev. B 40
1989
Earlier work this paper cites.
T. Kennedy, J. Phys.: Condens. Matter 2
1990
Earlier work this paper cites.
A. Klümper, A. Schadschneider, and J. Zittartz, J. Phys. A: Math. Gen. 24
1991
Earlier work this paper cites.
T. Kennedy and H. Tasaki, Phys. Rev. B 45
1992
Earlier work this paper cites.
M. Oshikawa, J. Phys.: Condens. Matter 4
1992
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, Comm. Math. Phys. 144
1992
Earlier work this paper cites.
K. Totsuka and M. Suzuki, J. Phys.: Condens. Matter 7
1995
Earlier work this paper cites.
Y. Nishiyama, N. Hatano, and M. Suzuki, J. Phys. Soc. Jpn. 64
1995
Earlier work this paper cites.
E. Dagotto and T. M. Rice, Science 271
1996
Earlier work this paper cites.
A. Kitazawa and K. Nomura, J. Phys. Soc. Jpn. 66
1997
Earlier work this paper cites.

S. Todo, M. Matsumoto, C. Yasuda, and H. Takayama, Phys. Rev. B 64
2001
Cited alongside, same era.
P. Calabrese and J. Cardy, JSTAT 2004
2004
Cited alongside, same era.
C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95
2005
Cited alongside, same era.
M. M. Wolf, G. Ortiz, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 97
2006
Cited alongside, same era.
D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum Inf. Comput. 7
2007
Cited alongside, same era.
G. Vidal, Phys. Rev. Lett. 98
2007
Cited alongside, same era.
F. Anfuso and A. Rosch, Phys. Rev. B 76
2007
Cited alongside, same era.
E. Berg, E. G. Dalla Torre, T. Giamarchi, and E. Altman, Phys. Rev. B 77
2008
Cited alongside, same era.
T. Hirano, H. Katsura, and Y. Hatsugai, Phys. Rev. B 77
2008
Cited alongside, same era.
R. Orús and G. Vidal, Phys. Rev. B 78
2008
Cited alongside, same era.
D. Pérez-García, M. Wolf, M. Sanz, F. Verstraete, and J. Cirac, Phys. Rev. Lett. 100
2008
Cited alongside, same era.
Z.-C. Gu and X.-G. Wen, Phys. Rev. B 80
2009
Cited alongside, same era.

F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Phys. Rev. B 81
2010
Closest in time.
M. Nakamura, E. J. Bergholtz, and J. Suorsa, Phys. Rev. B 81
2010
Closest in time.
H.-C. Jiang, S. Rachel, Z.-Y. Weng, S.-C. Zhang, and Z. Wang, Phys. Rev. B 82
2010
Closest in time.
D. Poilblanc, Phys. Rev. Lett. 105
2010
Closest in time.
D. Charrier, S. Capponi, M. Oshikawa, and P. Pujol, Phys. Rev. B 82
2010
Closest in time.
A. M. Turner, F. Pollmann, and E. Berg, Phys. Rev. B 83
2011
Closest in time.
N. Schuch, D. Pérez-García, and I. Cirac, Phys. Rev. B 84
2011
Closest in time.
K. Hasebe and K. Totsuka, Phys. Rev. B 84
2011
Closest in time.
K. Okunishi, Phys. Rev. B 83
2011
Closest in time.
A. M. Läuchli and J. Schliemann, ArXiv e-prints (2011), arXiv:eprint 1106.3419
2011
Closest in time.
T. Tonegawa, K. Okamoto, H. Nakano, T. Sakai, K. Nomura, and M. Kaburagi, J. Phys. Soc. Jpn. 80
2011
Closest in time.

alphaXiv searches the wider corpus for related work and actual follow-ups.

alphaXiv is searching for related work…

Reading the bibliography…