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Entanglement entropy of squeezed vacua on a lattice
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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.
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Adiabatic vacua from linear complex structures
Adiabatic number operators and vacua for coupled bosonic systems are constructed order by order from a linear recursion for complex structures, generalizing WKB and Lewis-Riesenfeld invariant methods beyond a single mode.
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