Coexistence of solutions in dynamical mean-field theory of the Mott transition

TL;DR

This paper investigates the finite-temperature metal-insulator transition in the paramagnetic Hubbard model using dynamical mean-field theory, demonstrating coexistence solutions via QMC and Exact Diagonalization, and analyzing discretization errors affecting QMC results.

Contribution

It provides a consistent approach to obtaining coexistence solutions in the Hubbard model using both QMC and Exact Diagonalization, highlighting the impact of discretization errors.

Findings

Coexistence solutions are obtainable via QMC and Exact Diagonalization.

Discretization errors in QMC explain difficulties near coexistence boundaries.

The study clarifies the finite-temperature Mott transition in the Hubbard model.

Abstract

In this paper, I discuss the finite-temperature metal-insulator transition of the paramagnetic Hubbard model within dynamical mean-field theory. I show that coexisting solutions, the hallmark of such a transition, can be obtained in a consistent way both from Quantum Monte Carlo (QMC) simulations and from the Exact Diagonalization method. I pay special attention to discretization errors within QMC. These errors explain why it is difficult to obtain the solutions by QMC close to the boundaries of the coexistence region.