Quantum Monte Carlo study of the 3D attractive Hubbard model

TL;DR

This study uses Quantum Monte Carlo simulations to analyze the 3D attractive Hubbard model, revealing a phase diagram with two key temperature scales and suggesting a hidden phase transition relevant to high-temperature superconductivity.

Contribution

It provides the first detailed finite-temperature phase diagram of the 3D attractive Hubbard model using Determinant Quantum Monte Carlo, highlighting two fundamental temperature scales and a potential hidden phase transition.

Findings

Identification of two temperature scales T* and Tc.

Evidence for a hidden phase transition.

Comparison with 2D case relevant for high-Tc superconductors.

Abstract

We study the three-dimensional (3D) attractive Hubbard model by means of the Determinant Quantum Monte Carlo method. This model is a prototype for the description of the smooth crossover between BCS superconductivity and Bose-Einstein condensation. By detailed finite-size scaling we extract the finite-temperature phase diagram of the model. In particular, we interpret the observed behavior according to a scenario of two fundamental temperature scales; T* associated with Cooper pair formation and Tc with condensation (giving rise to long-range superconducting order). Our results also indicate the presence of a recently conjectured phase transition hidden by the superconducting state. A comparison with the 2D case is briefly discussed, given its relevance for the physics of high-Tc cuprate superconductors.