## SciPost Submission Page

# Emergence of generalized hydrodynamics in the non-local Luttinger model

### by Per Moosavi

### Submission summary

As Contributors: | Per Moosavi |

Arxiv Link: | https://arxiv.org/abs/2003.10993v2 (pdf) |

Date submitted: | 2020-04-16 |

Submitted by: | Moosavi, Per |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Mathematical Physics |

Approach: | Theoretical |

### Abstract

We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 2 on 2020-6-20 Invited Report

### Strengths

1- Well-written paper, easy to read

2- A clear example of the emergence of Euler scale GHD

### Weaknesses

1- Fairly narrow in scope.

2-Contrary to interacting models like hard rods or reversible cellular automata where the emergence of GHD can be understood analytically, the methods used here rely on the non-interacting nature of the model. (of course, the underlying fermionic model is interacting, but at the end of the day, both the GHD and the ab-initio calculations are performed on the bosonized version)

3-The key features of GHD are interactions and the density dependence of the effective velocity, which are unfortunately gone here.

### Report

In this paper, the author studies the emergence of generalized hydrodynamics in the non-local Luttinger liquid model. As the non-local Luttinger liquid model is effectively non-interacting, non-equilibrium properties can be computed exactly at all times and length scales. This provides a useful playground to investigate the emergence of Euler scale hydrodynamics. This paper is well-written, and easy to follow. The results are interesting, though as I noted above some of the key ingredients of GHD due to interactions are absent in this model. Still, it's nice to see the emergence of Euler scale GHD, and the discussion of dispersion is valuable.

### Anonymous Report 1 on 2020-6-12 Invited Report

### Strengths

- the calculations are performed carefully, clearly and almost rigorously, with the non-rigorous steps properly pointed out.

- It brings out the physics of dispersion and its relation to the Euler scale very well.

### Weaknesses

- The techniques are is restricted to free models

### Report

In this paper, the author studies the non-local Luttinger liquid model from the perspective of its non-equilibrium dynamics and connection with generalised hydrodynamics.

The paper is extremely well written. The statement of the problem is clear, the calculations well presented, and the results clear. The problem and results are also interesting; they provide a further understanding of the emergence of hydrodynamics. The problem itself is of physical importance, it is a natural extension of the usual Luttinger liquid model with point-like interaction, and it has received some attention recently especially out of equilibrium. Showing the emergence of hydrodynamics is clearly an interesting problem for this model. The interest, here, is not the effects of interactions - as the model is essentially free (this is so from the viewpoint to the bosons or of the hydrodynamics, but interacting in the original fermions) - but rather the effects of dispersion. It is seen, in quite some detail, how and why dispersions effects, that are present because of the nonzero range of the fermion interaction potentials, go away in the Euler scaling limit. This is expected on physical grounds, but this paper provide quite explicit explanations and results.

A weak point of this paper is that it is restricted to free models. A strong point is that the calculations are performed carefully, clearly and almost rigorously, with the non-rigorous steps properly pointed out. Another strong point is that it brings out the physics of dispersion and its relation to the Euler scale very well.

I found only two typos: page 9 top [(2.6)ff], page 13 top (4.10)ff. Otherwise I do not have additional comment - all concepts are well addressed by the paper.

### Requested changes

no change except typos noted in report