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Local fermion density in inhomogeneous free-fermion chains: a discrete WKB approach
by Martín Zapata, Federico Finkel, Artemio González-López
Submission summary
| Authors (as registered SciPost users): | Artemio González-López |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2511.16473v2 (pdf) |
| Date submitted: | Feb. 11, 2026, 1:03 p.m. |
| Submitted by: | Artemio González-López |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We introduce a novel analytical approach for studying free-fermion (XX) chains with smoothly varying, site-dependent hoppings and magnetic fields. Building on a discrete WKB-like approximation applied directly to the recurrence relation for the single-particle eigenfunctions, we derive a closed-form expression for the local fermion density profile as a function of the Fermi energy, which is valid for arbitrary fillings, hopping amplitudes and magnetic fields. This formula reproduces the depletion and saturation effects observed in previous studies of inhomogeneous free-fermion chains, and provides a theoretical framework to understand entanglement entropy suppression in these models. We demonstrate the accuracy of our asymptotic formula in several chains with different hopping and magnetic field profiles. Our findings are thus the first step towards an analytical treatment of entanglement in free-fermion chains beyond the reach of conventional field-theoretic techniques.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
After carefully considering and answering the two referees' reports, we would like to submit a revised version of the paper, that we believe addresses their main suggestions and requirements. We trust that the revised version of our paper, that has already been published by the ArXiv (http://arxiv.org/abs/2511.16473), fully meets the publication standards of SciPost Physics.
List of changes
We have made the following changes:
- We implemented the minor correction in item 1 of the first referee's requested changes.
- We substantially reduced figure 1.
- We added a new Remark 5.1, providing a discussion of the LDA in the context of our work.
- We added two new references (now [19] and [35] in the paper's revised version).