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Phys. Rev. B 73, 245115 (2006) [10 pages]

Entanglement entropy and the Berry phase in the solid state

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S. Ryu
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA

Y. Hatsugai
Department of Applied Physics, University of Tokyo, Hongo Bunkyo-ku, Tokyo 113-8656, Japan

Received 11 January 2006; revised 16 May 2006; published 26 June 2006

Theentanglement entropy (von Neumann entropy) has been used to characterizethe complexity of many-body ground states in strongly correlated systems.In this paper, we try to establish a connection betweenthe lower bound of the von Neumann entropy and theBerry phase defined for quantum ground states. As an example,a family of translational invariant lattice free fermion systems withtwo bands separated by a finite gap is investigated. Weargue that, for one-dimensional (1D) cases, when the Berry phase(Zak's phase) of the occupied band is equal to ×(odd integer)and when the ground state respects a discrete unitary particle-holesymmetry (chiral symmetry), the entanglement entropy in the thermodynamic limitis at least larger than ln 2 (per boundary), i.e.,the entanglement entropy that corresponds to a maximally entangled pairof two qubits. We also discuss how this lower boundis related to vanishing of the expectation value of acertain nonlocal operator which creates a kink in 1D systems.

©2006 The American Physical Society

URL:	http://link.aps.org/doi/10.1103/PhysRevB.73.245115
DOI:	10.1103/PhysRevB.73.245115
PACS:	71.10.Fd; 73.43.-f; 03.65.Ud; 77.22.Ej 71.10.Fd Lattice fermion models (condensed matter) including Hubbard model, etc 73.43.-f Quantum Hall effects 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) 77.22.Ej Dielectric polarization and depolarization YEAR: 2006
KEYWORDS:	quantum entanglement, Berry phase, entropy, ground states, strongly correlated electron systems, fermion systems

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X. G. Wen, Phys. Rev. B 40, R7387 (1989);

ibid. 41, 9377 (1990)

T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002).
G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003).
H. Fan, V. Korepin, and V. Roychowdhury, Phys. Rev. Lett. 93, 227203 (2004).
S. Furukawa, G. Misguich, and M. Oshikawa, Phys. Rev. Lett. 96, 047211 (2006).
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, R1651 (1993);

48, 4442 (1993)

R. Resta, Rev. Mod. Phys. 66, 899 (1994).
M. den Nijs and K. Rommelse, Phys. Rev. B 40, 4709 (1989).
M. Nakamura and S. Todo, Phys. Rev. Lett. 89, 077204 (2002).
S. Ryu and Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002).
Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
J. Zak, Phys. Rev. Lett. 62, 2747 (1989).
S. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 167602 (2004).
N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997).
A. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, Rev. Mod. Phys. 60, 781 (1988).
N. Read and D. Green, Phys. Rev. B 61, 10267 (2000).
T. Senthil, M. P. A. Fisher, L. Balents, and C. Nayak, Phys. Rev. Lett. 81, 4704 (1998).
Y. Morita and Y. Hatsugai, Phys. Rev. B 62, 99 (2000).
Y. Hatsugai and S. Ryu, Phys. Rev. B 65, 212510 (2002).
M. M. Wolf, Phys. Rev. Lett. 96, 010404 (2006).
D. Gioev and I. Klich, Phys. Rev. Lett. 96, 100503 (2006).
G. Sundaram and Q. Niu, Phys. Rev. B 59, 14915 (1999).
D. Xiao, J. Shi, and Q. Niu, Phys. Rev. Lett. 95, 137204 (2005).
A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006).
M. Levin and X. G. Wen, Phys. Rev. Lett. 96, 110405 (2006).
W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).

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