Entanglement entropies for Lifshitz fermionic fields at finite density

Abstract: The entanglement entropies of an interval for the free fermionic spinless Schroedinger field theory at finite density and zero temperature are investigated. The interval is either on the line or at the beginning of the half line, when either Neumann or Dirichlet boundary conditions are imposed at the origin. We show that the entanglement entropies are finite functions of a dimensionless parameter proportional to the area of the rectangular region in the phase space identified by the Fermi momentum and the length of the interval. For the interval on the line, the entanglement entropy is a monotonically increasing function. Instead, for the interval on the half line, it displays an oscillatory behaviour related to the Friedel oscillations of the mean particle density at the entangling point. By employing the properties of the prolate spheroidal wave functions or the expansions of the tau functions of the kernels occurring in the spectral problems, determined by the two point function, we find analytic expressions for the expansions of the entanglement entropies in the asymptotic regimes of small and large area of the rectangular phase space region. Extending our analysis to a class of free fermionic Lifshitz models, we find that the parity of the Lifshitz exponent determines the properties of the bipartite entanglement.

HEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

( video )

Purdue HET

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