Abstract
Topological quantum phase transitions are numerically investigated in a spin-1/2 dimerized and frustrated Heisenberg chain by using infinite matrix product state representation with the infinite time evolving block decimation method. Quantum fidelity approach is employed to detect the degenerate ground states and quantum phase transitions. By calculating the long-range string order parameters, we find two topological Haldane phases characterized by two long-range string orders. Also, continuous and discontinuous behaviors of von Neumann entropy show that phase transitions between two topological Haldane phases are topologically continuous and discontinuous quantum phase transitions. For the topologically continuous phase transition, the central charge at the critical point is obtained as c = 1, which means that the topologically continuous quantum phase transition belongs to the Gaussian universality class.
Similar content being viewed by others
References
F. Verstraete, M.A. Martin-Delgado, J.I. Cirac, Phys. Rev. Lett. 92, 087201 (2004)
L. Amico, F. Baroni, A. Fubini, D. Patan’e, V. Tognetti, P. Verrucchi, Phys. Rev. A 74, 022322 (2006)
G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)
P. Calabrese, J. Cardy, J. Stat. Mech. 0406, 06002 (2004)
H.L. Haselgrove, M.A. Nielsen, T.J. Osborne, Phys. Rev. A 69, 032303 (2004)
H.-Q. Zhou, J.-H. Zhao, B. Li, Phys. Rev. E 41, 492002 (2008)
J.-H. Zhao, H.-L. Wang, B. Li, H.-Q. Zhou, Phys. Rev. E 82, 061127 (2010)
Y.H. Su, B.-Q. Hu, S.-H. Li, S.Y. Cho, Phys. Rev. E 88, 032110 (2013)
Y.-W. Dai, S.Y. Cho, Murray T. Batchelor, H.-Q. Zhou, Phys. Rev. E 89, 032110 (2014)
P.W. Anderson, Basic Notions of Condensed Matter Physics (Addison-Wesley, Reading, 1997)
S. Coleman, in An Introduction to Spontaneous Symmetry Breakdown and gauge Fields, Laws of Hadronic Matter, edited by A. Zichichi (Academic, New York, 1975)
M. den Nijs, K. Rommelse, Phys. Rev. B 40, 4709 (1989)
X.-Y. Feng, G.-M. Zhang, T. Xiang, Phys. Rev. Lett. 98, 087204 (2007)
H.D. Chen, Z. Nussinov, J. Phys. A 41, 075001 (2008)
F.C. Alcaraz, Y. Hatsugai, Phys. Rev. B 46, 13914 (1992)
A.K. Kolezhuk, U. Schollwöck, Phys. Rev. B 65, 100401 (2002)
K. Hida, Phys. Rev. B 45, 2207 (1992)
H.-H. Hung, C.-D. Gong, Phys. Rev. B 71, 13914 (2005)
S. Yamamoto, Phys. Rev. B 55, 3603 (1997)
Y.H. Su, S.Y. Cho, B. Li, H.L. Wang, H.-Q. Zhou, J. Phys. Soc. Jpn 81, 074003 (2012)
D.G. Shelton, A.A. Nersesyan, A.M. Ysvelik, Phys. Rev. B 53, 8521 (1996)
H. Tasaki, Phys. Rev. Lett. 66, 798 (1991)
H. Watanabe, K. Nomura, S. Takada, J. Phys. Soc. Jpn 62, 2845 (1993)
Y. Nishiyama, N. Hatano, M. Suzuki, J. Phys. Soc. Jpn 64, 1967 (1995)
S.R. White, Phys. Rev. B 53, 52 (1996)
E.H. Kim, G. Fáth, J. Slyom, D.J. Scalapino, Phys. Rev. B 62, 14965 (2000)
G. Fáth, Ö. Legeza, J. Sólyom, Phys. Rev. B 63, 134403 (2001)
M. Nakamura, S. Todo, Phys. Rev. Lett. 89, 077204 (2002)
H.-H. Hung, C.D. Gong, Y.-C. Chen, M.-F. Yang, Phys. Rev. B 73, 224433 (2006)
F. Anfuso, A. Rosch, Phys. Rev. B 76, 085124 (2007)
E.H. Kim, Ö. Legeza, J. Sólyom, Phys. Rev. B 77, 205121 (2008)
V.O. Garlea, A. Zheludev, L.P. Regnault, J.H. Chung, Y. Qiu, M. Boehm, K. Habicht, M. Meissner, Phys. Rev. Lett. 100, 037206 (2008)
G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)
G. Vidal, Phys. Rev. Lett. 91, 147902 (2003)
H.-L. Wang, A.-M. Chen, B. Li, H.-Q. Zhou, J. Phys. A 45, 015306 (2012)
R. Chitra, S. Pati, H.R. Krishnamurthy, D. Sen, S. Ramasesha, Phys. Rev. B 52, 6581 (1995)
V.M.L. Durga Prasad, S. Sahoo, S. Ramasesha, D. Sen, J. Phys.: Condens. Matter 25, 125603 (2013)
S. Shastry, B. Sutherland, Phys. Rev. Lett. 47, 964 (1981)
C.K. Majumdar, D.K. Ghosh, J. Math. Phys. 10, 1388 (1969)
Hai Tao Wang, Bo Li, Sam Young Cho, Phys. Rev. B 87, 054402 (2013)
T. Tonegawa, I. Harada, J. Math. Phys. 56, 2153 (1987)
K, Okamoto, K. Nomura. Phys. Lett. A 169, 433 (1992)
S. Eggert, Phys. Rev. B 54, R9612 (1996)
T. Kennedy, H. Tasaki, Phys. Rev. B 45, 304 (1992)
P. Calabrese, J. Cardy, J. Phys. A 42, 504005 (2009)
J. Cardy, Scaling and Renormalization in Statistical Physics (University of Oxford, Oxford, 1996)
L. Tagliacozzo, T.R. de Oliveira, S. Iblisdir, J.I. Latorre, Phys. Rev. B 78, 024410 (2008)
F. Pollmann, S. Mukerjee, A. Turner, J.E. Moore, Phys. Rev. Lett. 102, 255701 (2009)
G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)
C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, J., Wang, H. Quantum fidelity, string order parameter, and topological quantum phase transition in a spin-1/2 dimerized and frustrated Heisenberg chain. Eur. Phys. J. B 88, 256 (2015). https://doi.org/10.1140/epjb/e2015-60586-2
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2015-60586-2