Entanglement entropy and the Berry phase in solid states

Details Entanglement entropy and the Berry phase in solid states Entanglement entropy and the Berry phase in solid states

2006-01-11

arxiv.org/abs/cond-mat/0601237v3

Phys. Rev. B 73, 245115 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages, 4 figures, new references added

Scientific paper

10.1103/PhysRevB.73.245115

The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connection between the lower bound of the von Neumann entropy and the Berry phase defined for quantum ground states. As an example, a family of translational invariant lattice free fermion systems with two bands separated by a finite gap is investigated. We argue that, for one dimensional (1D) cases, when the Berry phase (Zak's phase) of the occupied band is equal to $\pi \times ({odd integer})$ and when the ground state respects a discrete unitary particle-hole symmetry (chiral symmetry), the entanglement entropy in the thermodynamic limit is at least larger than $\ln 2$ (per boundary), i.e., the entanglement entropy that corresponds to a maximally entangled pair of two qubits. We also discuss this lower bound is related to vanishing of the expectation value of a certain non-local operator which creates a kink in 1D systems.

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