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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
- Published as SciPost Phys. 11, 068 (2021)
|As Contributors:||Fabian Essler · Etienne Granet|
|Date submitted:||2021-08-16 14:14|
|Submitted by:||Granet, Etienne|
|Submitted to:||SciPost Physics|
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)
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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
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.