# Effective free-fermionic form factors and the XY spin chain

### Submission summary

 As Contributors: Oleksandr Gamayun Arxiv Link: https://arxiv.org/abs/2012.02079v4 (pdf) Date accepted: 2021-03-15 Date submitted: 2021-03-11 16:46 Submitted by: Gamayun, Oleksandr Submitted to: SciPost Physics Academic field: Physics Specialties: Mathematical Physics Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform the exact summation and present tau functions as Fredholm determinants in the thermodynamic limit. On the other hand simple expressions of form factors allow us to present the corresponding series as integrals of elementary functions. Using this approach we re-derive the asymptotics of static correlation functions of the XY quantum chain at finite temperature.

Published as SciPost Phys. 10, 070 (2021)

Dear Editor,

we have implemented changes asked by the Referees and hereby submit the revised manuscript.

Best Regards,
The Authors

### List of changes

1. Eq. (17): the index $\nu$ is inserted,
2. Ref. Commun Math Phys 129, 103–113(1990)) is added in Introduction and before Eq. (11).
3. A comment added after Eq. (8)
4. The 5th paragraph in the introduction is rewritten.
5. Small typos after Eqs. (59) and (63) are fixed
6. As the third Referee requested we have added Refs. [79], [80] and [86]
7. We have modified discussion after Eq. (53) and added Ref. [69]