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Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

by Oleksandr Gamayun, Oleg Lychkovskiy, Jean-Sébastien Caux

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Submission summary

Authors (as registered SciPost users): Oleksandr Gamayun · Oleg Lychkovskiy
Submission information
Preprint Link:  (pdf)
Date accepted: 2020-02-07
Date submitted: 2020-02-04 01:00
Submitted by: Gamayun, Oleksandr
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.

Author comments upon resubmission

We thank referees for careful reading of our manuscript. As requested we have corrected the typos and added references.

List of changes

Eqs. (7), (42), (66) and text below (86) are corrected. References [48] - [52] added.

Published as SciPost Phys. 8, 036 (2020)

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