Diego Pontello
(SISSA)

The last decades have seen groundbreaking progress in non-perturbative aspects of quantum field theory (QFT) using methods from quantum information theory. Most of these results have been so far restricted to relativistic QFT because constraints from Lorentz symmetry and causality play a key role in the above approaches. Much less is known in non-relativistic QFT, in particular, in the continuum QFT itself. In this talk, I will present the results of the entanglement entropies of an interval on the infinite line for a free fermionic spinless Schrödinger field theory at finite density, which is a non-relativistic model with Lifshitz exponent z=2. In this case, the entanglement spectrum can be exactly obtained and expressed in terms of prolate spheroidal wave functions. Analogously, the entropies can be also studied by means of the Fredholm determinant of the two-point correlator, which turns out to be the so-called tau function of a Painlevé V differential equation and it can be expressed in terms of Virasoro irregular conformal blocks of c=1. I will also discuss generalizations of these results to a class of free fermionic Lifshitz models labeled by integer dynamical exponent z.