Entanglement entropy and the Berry phase in the solid state

S. Ryu, Y. Hatsugai

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132 Scopus citations


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.

Original languageEnglish (US)
Article number245115
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number24
StatePublished - 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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