We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schrodinger field theory at finite density and zero temperature, which is a non-relativistic model with Lifshitz exponent z = 2. We prove that the entanglement entropies are finite functions of one dimensionless parameter proportional to the area of a rectangular region in the phase space determined by the Fermi momentum and the length of the interval. The entanglement entropy is a monotonically increasing function. By employing the properties of the prolate spheroidal wave functions of order zero or the asymptotic expansions of the tau function of the sine kernel, we find analytic expressions for the expansions of the entanglement entropies in the asymptotic regimes of small and large area of the rectangular region in the phase space. These expansions lead to prove that the analogue of the relativistic entropic C function is not monotonous. Extending our analyses to a class of free fermionic Lifshitz models labelled by their integer dynamical exponent z, we find that the parity of this exponent determines the properties of the bipartite entanglement for an interval on the line.

Entanglement entropies of an interval in the free Schrödinger field theory at finite density / Mintchev, Mihail; Pontello, Diego; Sartori, Alberto; Tonni, Erik. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2022:7(2022), pp. 1-81. [10.1007/JHEP07(2022)120]

Entanglement entropies of an interval in the free Schrödinger field theory at finite density

Pontello, Diego;Sartori, Alberto;Tonni, Erik
2022-01-01

Abstract

We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schrodinger field theory at finite density and zero temperature, which is a non-relativistic model with Lifshitz exponent z = 2. We prove that the entanglement entropies are finite functions of one dimensionless parameter proportional to the area of a rectangular region in the phase space determined by the Fermi momentum and the length of the interval. The entanglement entropy is a monotonically increasing function. By employing the properties of the prolate spheroidal wave functions of order zero or the asymptotic expansions of the tau function of the sine kernel, we find analytic expressions for the expansions of the entanglement entropies in the asymptotic regimes of small and large area of the rectangular region in the phase space. These expansions lead to prove that the analogue of the relativistic entropic C function is not monotonous. Extending our analyses to a class of free fermionic Lifshitz models labelled by their integer dynamical exponent z, we find that the parity of this exponent determines the properties of the bipartite entanglement for an interval on the line.
2022
2022
7
1
81
120
10.1007/JHEP07(2022)120
http://arxiv.org/abs/2201.04522v2
Mintchev, Mihail; Pontello, Diego; Sartori, Alberto; Tonni, Erik
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/131894
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