Entanglement entropy of squeezed vacua on a lattice

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 $Sp(2N,\mathbb{R})/\text{Isot}({J}_{0})$ 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 asymptotically bounded from above by the Kolmogorov-Sinai rate.