SciPost Submission Page
Entanglement flow in the Kane-Fisher quantum impurity problem
by Chunyu Tan, Yuxiao Hang, Stephan Haas, Hubert Saleur
Submission summary
| Authors (as registered SciPost users): | Chunyu Tan |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202410_00041v2 (pdf) |
| Date accepted: | 2024-11-18 |
| Date submitted: | 2024-11-10 05:31 |
| Submitted by: | Tan, Chunyu |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The problem of a local impurity in a Luttinger liquid, just like the anisotropic Kondo problem (of which it is technically a cousin), describes many different physical systems. As shown by Kane and Fisher, the presence of interactions profoundly modifies the physics familiar from Fermi liquid theory, and leads to non-intuitive features, best described in the Renormalization Group language (RG), such as flows towards healed or split fixed points. While this problem has been studied for many years using more traditional condensed matter approaches, it remains somewhat mysterious from the point of view of entanglement, both for technical and conceptual reasons. We propose and explore in this paper a new way to think of this important aspect. We use the realization of the Kane Fisher universality class provided by an XXZ spin chain with a modified bond strength between two sites and explore the difference of (Von Neumann) entanglement entropies of a region of length $\ell$ with the rest of the system - to which it is connected with a modified bond - in the cases when $\ell$ is even and odd. Surprisingly, we find out that this difference $\delta S\equiv S^e-S^o$ remains of $O(1)$ in the thermodynamic limit, and gives rise now, depending on the sign of the interactions, to "resonance" curves, interpolating between $-\ln 2$ and $0$, and depending on the product $\ell T_B$, where $1/T_B$ is a characteristic length scale akin to the Kondo length in Kondo problems. $\delta S$ can be interpreted as a measure of the hybridization of the left-over spin in odd length subsystems with the "bath" constituted by the rest of the chain. The problem is studied both numerically using DMRG and analytically near the healed and split fixed points. Interestingly - and in contrast with what happens in other impurity problems - $\delta S$ can, at least to lowest order, be tackled by conformal perturbation theory.
Author comments upon resubmission
Please find enclosed a slightly updated version of the manuscript. We have not understood what the second referee thought was not correct in the caption of figure 7. To be on the safe side however, we have made this caption more explicit, and given additional detail on the meaning of the axes.
We also have added some simple comments in the conclusion to make it more substantial. We are sorry we are not really able to provide a "more in depth discussion and perspective” beyond this, but our study of terms of O(1) is one of very few, and it is not clear to us yet how deep it might be. We think it is better to be short and honest, rather than indulge in vague speculations.
For the sake of efficiency, we are happy to have our paper considered for Sci. Post Core instead of Sci. Post Phys. In view of us having at least one entirely positive referee report recommending publication in Sci. Post Phys., we hope this will lead to quick acceptance.
We thank you and the referees for your time and effort.
Current status:
Editorial decision:
For Journal SciPost Physics Core: Publish
(status: Editorial decision fixed and (if required) accepted by authors)