Effective Hamiltonian based Monte Carlo for the BCS to BEC crossover in the attractive Hubbard model

TL;DR

This paper introduces an effective Hamiltonian-based real-space Monte Carlo method to study the BCS-BEC crossover in the 2D attractive Hubbard model, accurately capturing phase fluctuations, disorder effects, and various electronic phases.

Contribution

The authors develop and validate a classical Hamiltonian approach that efficiently models thermal fluctuations and disorder effects in superconductivity across the BCS-BEC crossover.

Findings

Accurate phase diagrams matching advanced numerical methods

Method effective in disordered systems

Identification of metallic, insulating, superconducting, and pseudogapped regions

Abstract

We present an effective Hamiltonian based real-space approach for studying the weak-coupling Bardeen-Cooper-Schrieffer (BCS) to the strong-coupling Bose-Einstein condensate (BEC) crossover in the two-dimensional attractive Hubbard model at finite temperatures. We introduce and justify an effective classical Hamiltonian to describe the thermal fluctuations of the relevant auxiliary fields. Our results for $T_c$ and phase diagrams compare very well with those obtained from more sophisticated and {\it cpu}-intensive numerical methods. We demonstrate that the method works in the presence of disorder and is useful for a real-space description of the effect of disorder on superconductivity. From a combined analysis of the superconducting order parameter, the distribution of auxiliary fields and the quasiparticle density of states, we identify the regions of metallic, insulating, superconducting and pseudogapped behavior. Our finding of the importance of phase fluctuations for the pseudogap behavior is consistent with the conclusions drawn from recent experiments on NbN superconductors. The method can be generalized to study superconductors with non-trivial order parameter symmetries by identifying the relevant auxiliary variables.