# Probing many-body localization in a disordered quantum dimer model on the honeycomb lattice

### Submission summary

 As Contributors: Francesca Pietracaprina Arxiv Link: https://arxiv.org/abs/2005.10233v2 (pdf) Date submitted: 2020-06-16 Submitted by: Pietracaprina, Francesca Submitted to: SciPost Physics Discipline: Physics Subject area: Quantum Physics Approaches: Theoretical, Computational

### Abstract

We numerically study the possibility of many-body localization transition in a disordered quantum dimer model on the honeycomb lattice. By using the peculiar constraints of this model and state-of-the-art exact diagonalization and time evolution methods, we probe both eigenstates and dynamical properties and conclude on the existence of a localization transition, on the available time and length scales (system sizes of up to N=108 sites). We critically discuss these results and their implications.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 2005.10233v2 on 16 June 2020

## Reports on this Submission

### Strengths

1-The authors consider a model that (to my knowledge) has not been considered before in the context of many-body localization (MBL), though bearing similarities to the previous study Ref. [48].
2-The authors use many different measures as a probe for MBL.
3-Relatively few studies into 2-dimensional MBL have been performed so far, the work is timely and relevant.
4-The findings are relevant to state-of-the-art experiments.

### Weaknesses

1-The authors do not clearly demonstrate that MBL properties survive in the thermodynamic limit - although it is not necessarily expected that this would be the case.

### Report

This work addresses the problem of many-body localization (MBL), which pertains to the interplay between disorder and interactions in many-body systems. At this point many numerical works have been devoted to MBL in one-dimensional systems, particularly in the archetypal model: the XXZ Heisenberg chain. There are strong indications that in this system there is a transition in the thermodynamic limit between an ergodic and a localized phase at a certain finite (model-dependent) strength of the disorder.

Of major interest is what happens in the case of two geometric dimensions (2D). Some theoretical approaches and recent experiments indicate that a "true" transition remains in this case, whereas some theoretical methods and our own recent numerics (Ref. [39]) suggest instead that in 2D the "transition" is more like a crossover, with an effective critical disorder that grows with system size.

The challenge for numerical approaches in 2D is that in even the simplest unconstrained many-body systems the Hilbert space growth exponentially in the number of sites $N$ as $2^N$. Since exact numerics ("unbiased" in the words of the authors) can handle up to 20-ish sites, this leaves the available system sizes prohibitively small. A way to circumvent this problem is by introducing constraints in the Hamiltonian, which reduces the scaling of the size of the Hilbert space with the number of sites.

The present manuscript considers such an approach in a constrained dimer model on a honeycomb lattice. The authors then proceed to apply a large distinct number of measures of the MBL transition to the model, including both static properties such as level statistics and entanglement, as well as dynamics. They argue that their results indicate an MBL transition in this model at a disorder value of $V \approx 20$-$25$.

This work represents a nice addition to the existing literature on MBL, in particular adding to the results in two dimensions where relatively few results are available, providing high-quality numerical results. In my view there is still a lot of potential for understanding MBL through the pathway of similar constrained models. I would recommend publication in SciPost Physics as the manuscript successfully addresses Expectation criteria 1 and 3.

1-I am confused concerning the discussion around Fig. 5. How are the black dashed lines computed here? What is their precise relation to the basis states?

2-I assume that the way the system is "sliced" for the bipartite entropy is not crucial for the results. Did the authors explicitly verify this?

3-A key question concerns the extrapolation of the results to large systems. The curves for the imbalance dynamics in Fig. 9 show quite a strong dependence on system size, seemingly much stronger than similar curves for the imbalance in 1D. I wonder if a crossover-type scenario along the lines of [Phys. Rev. B 99, 134305] might be a better explanation of the authors' results for this reason - although one should always be careful extrapolating from small systems of course. The authors fairly acknowledge such a possibility in the Conclusion, but perhaps it would be useful to explore this scenario in more detail.

### Requested changes

1-The axis labels are often tiny and hard to read. Please update the figures and make them more readable, using fewer columns if needed. Also, if there is a left and right panel, explain the left panel first (Fig. 2). If a figure has many colours, I recommend using a gradient (e.g. equally spaced colours from a "viridis" colourmap).

2-I'm not a big fan of this "biased/unbiased"-nomenclature, but if you must use it, please define clearly what is meant by this (exact vs. approximate approaches).

• validity: high
• significance: high
• originality: good
• clarity: good
• formatting: reasonable
• grammar: good