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Quantum quenches to the attractive one-dimensional Bose gas: exact results
by Lorenzo Piroli, Pasquale Calabrese, Fabian H. L. Essler
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|As Contributors:||Pasquale Calabrese · Fabian Essler · Lorenzo Piroli|
|Arxiv Link:||http://arxiv.org/abs/1604.08141v2 (pdf)|
|Date submitted:||2016-05-24 02:00|
|Submitted by:||Piroli, Lorenzo|
|Submitted to:||SciPost Physics|
We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function $g_2$.
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Anonymous Report 2 on 2016-6-27 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1604.08141v2, delivered 2016-06-26, doi: 10.21468/SciPost.Report.3
1. Extremely well written and free of typos.
2. Generously referenced.
3. Technical details of the computations presented in the manuscript are given
1. While the computations in the manuscript are technically impressive, the discussion of the physical consequences of these computations is not as expansive as it might be.
This manuscript studies the long time behaviour after a quantum quench in the Lieb-Liniger model, a model of a one-dimensional Bose gas. The particular quench studied takes the gas from c, the strength of its two-body interaction, zero to c finite and negative (i.e. the gas is quenched into its attractive regime).
The authors use the quench action to study this quench. The needed overlaps between the eigenstates of the post-quench Hamiltonian and the initial state of the gas had been determined by other authors. However some additional analysis of the overlaps in the case of states that are zero momentum n-strings by the authors was required. With the overlaps in hand, the authors are able to analyze the corresponding generalized TBA equations describing the steady state post-quench. Impressively, the authors are able to arrive at an analytical solution to these equations. Finally the authors use this solution to investigate g2, the pair correlation function (which can be obtained as a derivative of the generalized free energy by c). Interestingly the authors show that the density of higher bound states is reduced by increasing the strength of the attractive interaction.
I appreciate the careful presentation of results in this paper. It reads nicely and it is good to see
that all the details of the computations are presented in a comprehensible fashion. The one critique
that I do have is the sole focus on the steady state. It would be interested to understand more about
the approach to steady state. There have been suggestions in the literature (indeed, involving
one of the authors) of unusual entanglement entropy growth after a quench in systems with bound states.
It would be interesting to know if the authors felt something like this would occur here as well. I am not necessarily asking for a detailed computation. But some remarks to this end would be appreciated.
1. As I indicated, I would like to see some comments and/or analysis on the approach of the gas to the steady state post-quench.
Anonymous Report 1 on 2016-6-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1604.08141v2, delivered 2016-06-08, doi: 10.21468/SciPost.Report.2
1- Exact results.
2- Experimentally relevant.
3- Well written, clear exposition.
4- Exceptionally good (wide) list of references.
I don't see any weakness. It is true that most of the theoretical methods are already existing, but they are applied to a new situation, and there are certain steps that required new ideas.
This paper derives exact solutions for a specific quench problem in the attractive Lieb-Liniger model. The methods are simple generalizations of already available techniques, however, there are certain innovations and all results are new. The g2 local pair correlator is calculated numerically, and it is studied in the small coupling and large coupling limits. The physical consequences of the bound states are discussed. Maybe the most interesting is that g2 does not vanish in the infinite coupling limit. Whereas this is not necessarily surprising, it is useful that exact results are derived. I believe that later the results could be compared to experiments, thus strengthening the link between theory and experiment.
I don't request any changes, but I have a comment to the authors. It would be certainly interesting to consider the higher local correlators as well. For example g3. Maybe the three-strings would show up there in the large coupling limit?