Entanglement Entropy with Lifshitz Fermions

Submission summary

 As Contributors: Dion Hartmann · Kevin Kavanagh · Stefan Vandoren Arxiv Link: https://arxiv.org/abs/2104.10913v3 (pdf) Date accepted: 2021-07-23 Date submitted: 2021-07-06 07:35 Submitted by: Hartmann, Dion Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Quantum Physics Approach: Theoretical

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 $z$.

Published as SciPost Phys. 11, 031 (2021)

List of changes

1. In the introduction between equations 1 and 2 we added a sentence to clarify issues regarding non-integer z.
2. We fixed typos in the caption of figure 1.
3. We fixed a typo on page 3. We fixed a typo in equation 13.
4. We fixed a missing factor -i in equation 18.
5. We fixed a typo in eq 25. We fixed a typo below eq 26. We fixed a typo above eq 37.
6. We added three sentences to the paragraph after equation 37 to remark the universality of a result with respect to the partitioning of our system.
7. We fixed a typo in the caption of figure 2.
8. We fixed a typo in the axis labels of figure 3.
9. We added two sentences to the first paragraph of section 4 to remark other approaches not taken in the present paper.
10. We added equation 46 and two remarks just before it to clarify on the derivation of g.
11. We added some clarifying remarks below equation 53 and refer to the appendix to be more self-contained with regards to the derivation of g.
12. We added a clarification regarding the geodesic above equation 62.
13. We fixed a typo in the last sentence of section 4.
14. We added a remark to the first paragraph of section 5 highlighting again the universality with respect to the partitioning.
15. We added an appendix to be more self-contained with regards to the derivation of g.
16. We abbreviated several occurences of entanglement entropy to EE.