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Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model

by Etienne Granet and Fabian H. L. Essler

Submission summary

As Contributors: Fabian Essler · Etienne Granet
Preprint link: scipost_202103_00015v2
Date accepted: 2021-08-31
Date submitted: 2021-08-16 14:14
Submitted by: Granet, Etienne
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical

Abstract

We consider the time evolution of local observables after an interaction quench in the repulsive Lieb-Liniger model. The system is initialized in the ground state for vanishing interaction and then time-evolved with the Lieb-Liniger Hamiltonian for large, finite interacting strength $c$. We employ the Quench Action approach to express the full time evolution of local observables in terms of sums over energy eigenstates and then derive the leading terms of a $1/c$ expansion for several one and two-point functions as a function of time $t>0$ after the quantum quench. We observe delicate cancellations of contributions to the spectral sums that depend on the details of the choice of representative state in the Quench Action approach and our final results are independent of this choice. Our results provide a highly non-trivial confirmation of the typicality assumptions underlying the Quench Action approach.

Published as SciPost Phys. 11, 068 (2021)



Author comments upon resubmission

We thank the editor and the referee for the decision on the paper. We answered to the referee's question below their report. In the new version, we added the recommended references at the end of the first paragraph of the conclusion, which is the only modification.

Best regards,
Etienne Granet

Submission & Refereeing History

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Resubmission scipost_202103_00015v2 on 16 August 2021

Reports on this Submission

Anonymous Report 1 on 2021-8-26 (Contributed Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202103_00015v2, delivered 2021-08-26, doi: 10.21468/SciPost.Report.3455

Report

The authors determine relaxation of three quantities of interest in the integrable Lieb-Liniger model. They employ a 1/c expansion in order to deal with the significant challenge to deal with the large spectral sums needed analyse time dependent quanties. In this way they arrive at leading orders exact expressions for the time evolution of (i) the one-point function of the interaction potential, (ii) the density-density correlation function and (iii) the steady-state expectation value of the two-point function of the interaction potential, all after a BEC groundstate quench.

The results in this paper are derived with a very high level of technical competency, and despite its technical nature is very well written. The paper will of broad interest to the quantum dynamics community. I recommend publication without further revision.

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