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Entanglement Entropy with Lifshitz Fermions
by Dion Hartmann, Kevin Kavanagh, Stefan Vandoren
Submission summary
| Authors (as registered SciPost users): | Dion Hartmann · Kevin Kavanagh · Stefan Vandoren |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2104.10913v3 (pdf) |
| Date accepted: | July 23, 2021 |
| Date submitted: | July 6, 2021, 7:35 a.m. |
| Submitted by: | Dion Hartmann |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| 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 $z$.
List of changes
- In the introduction between equations 1 and 2 we added a sentence to clarify issues regarding non-integer z.
- We fixed typos in the caption of figure 1.
- We fixed a typo on page 3. We fixed a typo in equation 13.
- We fixed a missing factor -i in equation 18.
- We fixed a typo in eq 25. We fixed a typo below eq 26. We fixed a typo above eq 37.
- 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.
- We fixed a typo in the caption of figure 2.
- We fixed a typo in the axis labels of figure 3.
- We added two sentences to the first paragraph of section 4 to remark other approaches not taken in the present paper.
- We added equation 46 and two remarks just before it to clarify on the derivation of g.
- 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.
- We added a clarification regarding the geodesic above equation 62.
- We fixed a typo in the last sentence of section 4.
- We added a remark to the first paragraph of section 5 highlighting again the universality with respect to the partitioning.
- We added an appendix to be more self-contained with regards to the derivation of g.
- We abbreviated several occurences of entanglement entropy to EE.
Published as SciPost Phys. 11, 031 (2021)