Entanglement entropy and the Berry phase in the solid state

N/ACitations
Citations of this article
100Readers
Mendeley users who have this article in their library.
Get full text

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.

Cite

CITATION STYLE

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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free