SciPost Submission Page
On computing non-equilibrium dynamics following a quench
by Neil J. Robinson, Albertus J. J. M. de Klerk, Jean-Sébastien Caux
|As Contributors:||Neil Robinson · Albertus de Klerk|
|Arxiv Link:||https://arxiv.org/abs/1911.11101v2 (pdf)|
|Date submitted:||2020-11-22 19:36|
|Submitted by:||de Klerk, Albertus|
|Submitted to:||SciPost Physics|
Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2021-1-19 Invited Report
1. Novel method to solve 1d Bose gas for nontrivial interactions
2. Very detailed study of convergence
3. Method can be extended to a large claass of other systems
1. For the Bose gas, the number of the particles that can be treated with the method is relatively small. It is not clear that the method can be extended to more than a dozen particles, which severely restricts its applicability.
This paper introduces a new version of the truncated Hamiltonian method for the Bose gas. The main advance consists of a different truncation scheme, which prioritizes eigenstates with high overlap with the initial state, together with an improved renormalisation group method. The paper is a proof-of-principle investigation, and demonstrates a substantial improvement in convergence and accuracy. Despite the limitation in particle number, the results represent a significant and non-trivial advance over previously used approaches. I consider the paper fully suitably for Scipost Physics, and recommend its publication in the present form.
No changes requested.
Anonymous Report 1 on 2020-12-23 Invited Report
Development of a new numerical method with potentially many applications
I do not like to list weaknesses
In this paper, the authors introduce a new numerical approach to study the quench dynamics of integrable systems (with the possibility to extend to non integrable ones). The method is non-perturbative and it is inspired by TCSA in field theory, but it goes beyond it in many respects: 1) it preferentially generates the states with high overlaps for a quantum quench 2) it uses the basis of an interacting model 3) it encapsulates the most relevant states by means of a “high overlap states truncation scheme”. The method explained in a very detailed manner with a large number of convincing tests for a prototypical quench within the Lieb-Liniger model. It is surely not very useful to further summarise the results of a 50 pages long paper here, thus I move directly to the comments
The paper is well written and original. The ideas are extremely interesting and have a wide range of applications. Some results are presented for a specific interaction quench in the Lieb-Liniger model, but this is only one of the many possible applications. Similar ideas can be used beyond the Bose gas, for example also in the presence of string states and for non-integrable Hamiltonians, although there are some technical difficulties to overcome before addressing also these interesting problems. However, l I believe that the method is of large interest for the community even if it would only apply to the Bose gas, as proved here.
In conclusion, I think this paper is very good, and should be published in SciPost. Anyhow, I have a minor proposal that the authors could consider to implement or at least comment before publication (I do not need to see the paper again, I am sure that the authors reaction will be appropriate).
From the numerically calculated overlaps, the authors can easily construct a Bethe representative state (in the quench action language) and from this use the quasiparticle picture to reconstruct the time evolution of the entanglement entropy. I think that the addition of this result (here or in another paper if it takes too long) will nicely complement the presented predictions for local observables. Furthermore, they can also trivially determine the diagonal entropy and explore the relation between diagonal and thermodynamic entropy in the case the post-quench states are not parity invariant.