# Thermodynamics of the metal-insulator transition in the extended Hubbard model

### Submission summary

 As Contributors: Malte Schüler Arxiv Link: https://arxiv.org/abs/1903.09947v2 Date submitted: 2019-04-09 Submitted by: Schüler, Malte Submitted to: SciPost Physics Domain(s): Theoretical Subject area: Condensed Matter Physics - Theory

### Abstract

In contrast to the Hubbard model, the extended Hubbard model, which additionally accounts for non-local interactions, lacks systemic studies of thermodynamic properties especially across the metal-insulator transition. Using a variational principle, we perform such a systematic study and describe how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator. The thermodynamics reveal that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials.

###### Current status:
Has been resubmitted

### Ontology / Topics

See full Ontology or Topics database.

### Submission & Refereeing History

Resubmission 1903.09947v3 on 3 June 2019
Submission 1903.09947v2 on 9 April 2019

## Reports on this Submission

### Strengths

In this manuscript the authors study thermodynamic properties of the extended Hubbard model in 2D square lattice. This analysis is potentially important for further progress in understanding the extended Hubbard model, as there are no systematic analysis for such model yet.
The authors use the varioational method and map the original extended Hubbard model to the effective Hubbard model which they can solve using DQMC.
One of the main findings of this paper is that the authors claim that there is a first order metal-insulator transition induced by non-local intersite interactions V, observed as jumps in the double-occupancy and entropy analysis.

### Weaknesses

The major claim of this paper is based on the very small jumps in the double occupancy and entropy~10^-4. It is really not clear whether it is a numerical artifact, the noise, or the artifact of the particular variational method employed in this paper.
The authors state that they do not observe such first order transition in variational method is used only for the U term (with no hopping renormalization). Hence, it is not clear how valid this varioational approach is, some benchmarking is really necessary.
For this reason I am reluctant to recommend this paper for publication.

### Report

I am reluctant to recommend this paper for publication.

### Requested changes

1. The authors should say explicitly how the entropy calculations was done.
2. In Fig. 4 and Fig. 5, the data are presented in $t_tilde$ and $U_tilde$ paramter space. It is really not clear how these numbers are related to real U and t values.
3. The authors claim that they find the band broadening effect of non-local interactions V. Their claim is based on some speculations of free energy behavior in t_tilde parameter space. If the authors mean they see a similar effect as in REf.https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.245130, they should perhaps find a better way to support their claim.
4. Why in eq. 7, the original lattice dispersion function $\epsilon_k$ and not for the effective Hubbard model $\tilde{\epsilon_k}$ is used.
5. Why the energy units (hopping $t$) are changes through the paper? In Fig. 6 the authors used $t=1.26$ and in Fig. 9, $t=1$ is used. This way your are studying the original extended Hubbard model for different bandwidth values.

• validity: low
• significance: ok
• originality: good
• clarity: low
• formatting: perfect
• grammar: perfect

### Strengths

1 - An interesting study on thermodynamics of the metal-insulator transition in the extended Hubbard model.
2 - Comprehensive numerical calculation that clarifies how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator.
3 – Numerical indications that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials.

### Weaknesses

1- Numerically very subtle calculation.

### Report

This work takes a variational approach to study the extended Hubbard model having interactions between electrons on different lattice sites. In contrast with the on-site Hubbard model, the properties of the extended Hubbard model are far less well understood. Especially, as is emphasized by the authors, systematic studies of thermodynamic properties are rare and reference data for detailed comparisons and benchmarks between methods is missing.
In the phase diagram, there is a phase transition from Fermi-liquid to insulator. The authors focus on the so-called Slater regime with small interactions. There are two mechanisms how non-local interactions suppress correlation effects. Namely, the non-local interactions effectively reduce (enhance) the local interaction (transfer hopping) in the Fermi liquid (insulator). They found that the competition of these two mechanisms drives a first-order metal-insulator transition.
The authors perform a comprehensive numerical study and present a variety of plots which corroborate their claim. This work will stimulate further interest in the extended Hubbard model and I would like to recommend publication in SciPost Physics.

### Requested changes

It would be better to explicitly mention that the change in the double occupancy plotted in Fig. 2 is very small. Even in the case of V/t=0.3, the jump is only 0.0003. The energy scale of the structure plotted in Fig.4 is also 0.0001. I understand that they performed the calculation very carefully, and the variational method which they employed worked quite successfully in their previous works. However, their approach is not the unique way to map the extended Hubbard model onto the Hubbard model. We may think about the possibility where {\tilde U} in the effective model has \omega dependence. I wonder how the present result is modified when we improve the mapping from the extended Hubbard model to the on-site Hubbard model.

• validity: high
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: excellent