Abstract
Without any knowledge of the symmetry existing in a system, we derive the exact forms of the order parameters which show long-range correlations in the ground state of the one-dimensional (1D) extended Hubbard model using a quantum information approach. Our work demonstrates that the quantum information approach can help us to find the explicit form of the order parameter, which could not be derived systematically via traditional methods in the condensed matter theory.
Similar content being viewed by others
References
G.D. Mahan, Many Particle Physics (Kluwer Academic/Plenum Publishers, New York, 2000)
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2000)
S. Furukawa, G. Misguich, M. Oshikawa, Phys. Rev. Lett. 96, 047211 (2006)
C.L. Henley, H.J. Changlani, J. Stat. Mech. 2014, P11002 (2014)
S.-A. Cheong, C.L. Henley, Phys. Rev. B 79, 212402 (2009)
S.J. Gu, W.C. Yu, H.Q. Lin, Ann. Phys. 336, 118 (2013)
G.W. Hayden, Z.G. Soos, Phys. Rev. B 38, 6075 (1988)
D.K. Campbell, T.A. DeGrand, S. Mazumdar, Phys. Rev. Lett. 52, 1717 (1984)
H.J. Schulz, Phys. Rev. Lett. 64, 2831 (1990)
M.M. Wolf, F. Verstraete, M.B. Hastings, J.I. Cirac, Phys. Rev. Lett. 100, 070502 (2008)
S.J. Gu, C.P. Sun, H.Q. Lin, J. Phys. A 41, 025002 (2008)
V.J. Emery, in Highly Conducting One Dimensional Solids, edited by J.T. Devreese et al. (Plenum, New York, 1979), pp. 247–303
J. Solyom, Adv. Phys. 28, 201 (1979)
V.J. Emery, Phys. Rev. B 14, 2989 (1976)
M. Fowler, Phys. Rev. B 17, 2989 (1978)
G.S. Tian, Phys. Rev. B 45, 3145 (1992)
H.Q. Lin, E.R. Gagliano, D.K. Campbell, E.H. Fradkin, J.E. Gubernatis, in The Hubbard Model: Its Physics and Mathematical Physics, edited by D. Baeriswyl et al. (Plenum, New York, 1995), pp. 315–327
H.Q. Lin, D.K. Campbell, R.T. Clay, Chin. J. Phys. 38, 1 (2000)
J.E. Hirsch, Phys. Rev. Lett. 53, 2327 (1984)
S.J. Gu, S.S. Deng, Y.Q. Li, H.Q. Lin, Phys. Rev. Lett. 93, 086402 (2004)
S.S. Deng, S.J. Gu, H.Q. Lin, Phys. Rev. B 74, 045103 (2006)
M. Nakamura, J. Phys. Soc. Jpn 68, 3123 (1999)
M. Nakamura, Phys. Rev. B 61, 16377 (2000)
E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)
E. Jeckelmann, Phys. Rev. Lett. 91, 089702 (2003)
P. Sengupta, A.W. Sandvik, D.K. Campbell, Phys. Rev. B 65, 155113 (2002)
A.W. Sandvik, L. Balents, D.K. Campbell, Phys. Rev. Lett. 92, 236401 (2004)
Y.Z. Zhang, Phys. Rev. Lett. 92, 246404 (2004)
S. Ejima, S. Nishimoto, Phys. Rev. Lett. 99, 216403 (2007)
M. Tsuchiizu, A. Furusaki, Phys. Rev. Lett. 88, 056402 (2002)
M. Tsuchiizu, A. Furusaki, Phys. Rev. B 69, 035103 (2004)
C. Mund, O. Legeza, R.M. Noack, Phys. Rev. B 79, 245130 (2009)
G.-H. Liu, C.-H. Wang, Commun. Theor. Phys. 55, 702 (2011)
Y.C. Li, Z.G. Yuan, Phys. Lett. A 380, 272 (2016)
J. Hubbard, Proc. Roy. Soc. A 276, 238 (1963)
M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963)
J. Kanamori, Prog. Theor. Phys. 30, 275 (1963)
P.D. Sacramento, Y.C. Li, S.J. Gu, J.M.P. Carmelo, Eur. Phys. J. B 86, 507 (2013)
G. Misguich, C. Lhuillier, in Frustrated spin systems, edited by H.T. Diep (World-Scientific, Singapore, 2005)
T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)
A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416, 608 (2002)
L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)
H.T. Quan, Z. Song, X.F. Liu, P. Zanardi, C.P. Sun, Phys. Rev. Lett. 96, 140604 (2006)
P. Zanardi, N. Paunković, Phys. Rev. E 74, 031123 (2006)
S.J. Gu, Int. J. Mod. Phys. B 24, 4371 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, W., Gu, SJ. & Lin, HQ. Density matrix spectra and order parameters in the 1D extended Hubbard model. Eur. Phys. J. B 89, 212 (2016). https://doi.org/10.1140/epjb/e2016-70361-6
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2016-70361-6