Entanglement entropy and the Berry phase in the solid state

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Abstract

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 π× (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 how this lower bound is related to vanishing of the expectation value of a certain nonlocal operator which creates a kink in 1D systems. © 2006 The American Physical Society.

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APA

Ryu, S., & Hatsugai, Y. (2006). Entanglement entropy and the Berry phase in the solid state. Physical Review B - Condensed Matter and Materials Physics, 73(24). https://doi.org/10.1103/PhysRevB.73.245115

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