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Exact Thermal Properties of free-fermionic Spin Chains

by Michał Białończyk, Fernando Javier Gómez-Ruiz, Adolfo del Campo

Submission summary

As Contributors: Michał Białończyk · Fernando Gómez-Ruiz
Preprint link: scipost_202104_00014v3
Date accepted: 2021-07-06
Date submitted: 2021-06-30 15:32
Submitted by: Białończyk, Michał
Submitted to: SciPost Physics
Academic field: Physics
  • Mathematical Physics
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.

Published as SciPost Phys. 11, 013 (2021)

Author comments upon resubmission

Dear SciPost Editorial College,
We address here the comments in the Editorial Report:

Editors write: “The Scipost editorial college unanimously agreed that your manuscript
deserved to be published on Scipost. However, the college thinks that the title (and bit also
the emphasis) is misleading about the content of the paper. A paper with title "Exact
Thermal Properties of Integrable Spin Chains" cannot be based only on the analysis of a free
fermionic chain. The college asks then to reconsider the title of the paper into something like
"Exact Thermal Properties of free-fermionic Spin Chains", stressing that it would be very
interesting to understand in more generality which of properties discussed here survive to
the addition of (integrable) interactions.”

Authors’ Reply: Following the suggestion by the editors, we hereby resubmit the
manuscript with the modified title "Exact Thermal Properties of free-fermionic Spin Chains",

Editors write: “Furthermore, some members of the college noticed that while the
bibliography is rather complete on the free fermion side, there is not a single reference to the
large literature on full-counting statistics in truly interacting integrable models (like XXZ spinchains
and 1D Bose gas). The paper will surely benefit of the inclusion of a few references on
the subject .”

Authors’ Reply: We appreciate the suggestion from some college members to include new
references about XXZ spin-chains and 1D Bose gas. However, since our manuscript describes
the thermal properties of the anisotropic XY spin chain in the Ising universal class, it would
be self-contradictory to include references from broader topic while restricting the title.
Therefore, we consider the bibliography complete and covering all relevant works in such
systems, beyond the scope of the manuscript.

Finally, we would appreciate if the editors could handle the manuscript promptly to prevent
further delays. Please note between the reception of final referee comments and editorial
decision a period of 34 days passed by in which further results have been reported by other
authors, including some by members of the SciPost Editorial College. This is thus a timely
submission that would greatly benefit from a prompt publication.

Sincerely, the authors

List of changes

- Change of the title (from ,,Exact Thermal Properties of Integrable Spin Chains") to ,,Exact Thermal Properties of free-fermionic Spin Chains''

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