Entanglement entropy of squeezed vacua on a lattice

TL;DR

This paper derives a formula for the entanglement entropy of squeezed states on a lattice, linking it to complex structures and symplectic group theory, with applications to area laws and entropy growth rates.

Contribution

It introduces a novel formula for entanglement entropy of squeezed states using complex structures and symplectic group theory, with practical applications to lattice scalar fields.

Findings

Derives an area law for ground state entanglement entropy.

Calculates entropy growth rate in unstable systems.

Shows entropy growth is bounded by Kolmogorov-Sinai rate.

Abstract

We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with group-theoretical coherent states of the symplectic group and the relation between the coset Sp(2N,R)/Isot(J_0) and the space of complex structures. We present two applications of the new formula: (i) we derive the area law for the ground state of a scalar field on a generic lattice in the limit of small speed of sound, (ii) we compute the rate of growth of the entanglement entropy in the presence of an instability and show that it is bounded from above by the Kolmogorov-Sinai rate.