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Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

by Etienne Granet, Maurizio Fagotti, Fabian H. L. Essler

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Submission summary

Authors (as registered SciPost users): Fabian Essler · Etienne Granet
Submission information
Preprint Link: scipost_202003_00052v3  (pdf)
Date accepted: 2020-08-24
Date submitted: 2020-08-10 10:16
Submitted by: Granet, Etienne
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Mathematical Physics
  • Quantum Physics


We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

Published as SciPost Phys. 9, 033 (2020)

Author comments upon resubmission

We thank the referees again for their careful reading of the manuscript, and for recommending publication.
We corrected the few typos noticed by one of the three referees, which were the only requested changes.

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