Entanglement Entropy with Lifshitz Fermions

TL;DR

This paper explores how entanglement entropy in Lifshitz fermions varies with the scaling exponent z, revealing distinct behaviors for even and odd z, and employs lattice and holographic methods for analysis.

Contribution

It uncovers the parity-dependent behavior of entanglement entropy in Lifshitz fermions and applies both lattice correlation and holographic cMERA techniques for analysis.

Findings

Entanglement entropy vanishes for even z in the ground state.

For odd z, entanglement entropy matches the relativistic case with z=1.

Temperature effects diminish the even-odd parity distinction at high temperatures.

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 $z$.