Abstract
We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent z. Remarkably, in the ground state the entanglement entropy vanishes for even values of z, whereas for odd values it is independent of z and equal to the relativistic case with z=1. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of z and T which we plot using the lattice correlation method. The dependence on the even- or oddness of z still shows for small temperatures, but is washed out for large temperatures or large values of z.
Highlights
In this paper, we study entanglement properties of Dirac-Lifshitz fermions, with dispersion relations of the form: ω2k = α2k2z + m2, (1)with ω, k and m related to frequency, momentum and mass, with units specified
We introduce briefly the continuous Multi-scale Entanglement Renormalisation Ansatz which produces the elements necessary to calculate the entanglement entropy (EE) via holographic techniques
We have studied the EE between fermions with a Lifshitz scaling symmetry in both continuous and discrete models
Summary
We study entanglement properties of Dirac-Lifshitz fermions, with dispersion relations of the form: ω2k = α2k2z + m2 ,. The EE is independent of z, i.e. all odd values for z give the same result as for z = 1 This is very different from Lifshitz bosons, where the EE grows with z as expected from the lattice approach, since higher values of z indicate longer range correlators across the entanglement regions. Notice that this is consistent with the scaling weight (z − 1)/2 for a scalar field in 1+1 dimensions The result for this Fourier transform is formally valid for all values of z by analytic continuation of the Gamma function.
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