Variational Monte Carlo Study of Spin-Gapped Normal State and BCS-BEC Crossover in Two-Dimensional Attractive Hubbard Model

TL;DR

This study uses variational Monte Carlo methods to explore the normal, superconducting, and charge-density-wave states in a two-dimensional attractive Hubbard model, revealing a spin-gap transition and a BCS-BEC crossover.

Contribution

It introduces an interspinon binding factor in trial wave functions and demonstrates a first-order spin-gap transition and a smooth BCS-BEC crossover in the model.

Findings

First-order spin-gap transition at critical interaction strength.

Smooth crossover from BCS to BEC superconductivity as interaction increases.

Superconductivity driven by kinetic energy gain in the strong-coupling regime.

Abstract

We study properties of normal, superconducting (SC) and CDW states for an attractive Hubbard model on the square lattice, using a variational Monte Carlo method. In trial wave functions, we introduce an interspinon binding factor, indispensable to induce a spin-gap transition in the normal state, in addition to the onsite attractive and intersite repulsive factors. It is found that, in the normal state, as the interaction strength $|U|/t$ increases, a first-order spin-gap transition arises at $|U_{\rm c}|\sim W$ ($W$: band width) from a Fermi liquid to a spin-gapped state, which is conductive through hopping of doublons. In the SC state, we confirm by analysis of various quantities that the mechanism of superconductivity undergoes a smooth crossover at around $|U_{\ma{co}}|\sim |U_{\rm c}|$ from a BCS type to a Bose-Einstein condensation (BEC) type, as $|U|/t$ increases. For $|U|<|U_{\ma{co}}|$, quantities such as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit behavior of $\sim \exp(-t/|U|)$, as expected from the BCS theory. For $|U|>|U_{\ma{co}}|$, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as $\sim t^2/|U|\propto T_{\rm c}$, as expected in a bosonic scheme. In this regime, the SC transition is induced by a gain in kinetic energy, in contrast with the BCS theory. We refer to the relevance to the pseudogap in cuprate superconductors.