## SciPost Submission Page

# Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

### by Márton Mestyán, Vincenzo Alba

### Submission summary

As Contributors: | Márton Mestyán |

Arxiv Link: | https://arxiv.org/abs/1905.03206v2 |

Date submitted: | 2019-07-22 |

Submitted by: | Mestyán, Márton |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approach: | Theoretical |

### Abstract

The so-called flea gas is an elementary yet very powerful method that allows the simulation of the out-of-equilibrium dynamics after quantum quenches in integrable systems. Here we show that, after supplementing it with minimal information about the initial state correlations, the flea gas provides a versatile tool to simulate the dynamics of entanglement-related quantities. The method can be applied to any quantum integrable system and to a large class of initial states. Moreover, the efficiency of the method does not depend on the choice of the subsystem configuration. Here we implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. We compute the time evolution of the entanglement entropy and the mutual information in these quenches, providing strong confirmation of recent analytical results obtained using the Generalized Hydrodynamics approach. The method also allows us to obtain the full-time dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2019-8-27 Invited Report

### Strengths

1. timely subject exploring an effective approach to the non-equilibrium dynamics of quantum integrable systems

2. displays application of the molecular dynamics methods to the quantum lattice models

3. raises an interesting question on analytical derivation of the flea gas dynamics for the XXZ spin chain

### Weaknesses

1. lack of physical explanation why flea gas method is applicable to the XXZ spin chain, see the report for the details.

### Report

The authors apply the flea gas method, introduced and studied previously for the continuum models, to the dynamics of the XXZ spin chain. They focus on the entanglement spreading and compare the results of the simulations to the GHD at the Euler scale. The results suggest that the flea gas method is applicable in the lattice settings.

The paper is well written and the exposition of the subject, method and results is very good. Still, there are few points that I would like the authors to address.

1) page 3: The statement that the initial state is described by the GGE describing the long time limit is confusing. Please explain.

2) page 9: The bare velocity is used to uniquely distinguish different hard-rods. This requires however a Pauli-like principle in the system. Please comment on this.

3) page 9 and other places: the authors refer to $\rho(v(v_b) - v(w))$ or similar expressions as giving the number of scattering events per unit time. The units however does not match. Please correct.

4) page 10: following the discussion the flea gas dynamics seems inappropriate for the XXZ spin chain because the dressing can change the ordering of two velocities. Still the results suggest that the resulting dynamics is correct. I would like the authors to expand on this briefly answering or commenting on the following questions:

- how strong is the violation of the monotonicity?

- how does it change the dynamics?

- why is this effect negligible in the situations studied?

- are there situations in which this effect would be stronger?

5) page 12: what values does index $\alpha$ take in the flea gas algorithm, figure 2?

6) page 14: it is unclear if in figs. 4 e) & f) plotted are results of a single simulation or an average of many simulations. Please correct.

7) page 15: please explain what happens to the term with an explicit t dependence in (2) when writing it in the $l/t \rightarrow 0$ limit as in (33).

I would like the authors to address these questions before suggesting the publication of this work.

### Requested changes

Beside the issues mentioned in the report there are few smaller things:

8) page 2: the authors write "In (2), $v_{\alpha, \lambda}$ are these velocities". I find this sentence confusing/unnecessary.

9) page 4: is there a particular reason why the initial state of the form $|N, \theta\rangle \otimes |D\rangle$ is interesting?

10) page 8: a typo in the first paragraph "... to study the this quench [50,51]."

11) page 10: in the first paragraph first $\nu$ then $\lambda$ are used to refer to apparently the same particle

12) page 11: von Neumann entropy -> von Neumann entanglement entropy