Quantum Monte Carlo calculation of critical temperature of flat-band superconductivity in the Lieb-lattice Hubbard model

Abstract

We investigate a superconducting transition in the attractive Hubbard model on the Lieb lattice at the half-filled flat band with linear band-touching. Using the determinant quantum Monte Carlo simulations, we estimate the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for the onsite interaction |U|=1 based on the universal relation with the superfluid weight. We also perform a finite-size scaling analysis of the pair-field structure factor, examining its consistency with the BKT transition. Our estimate of the transition temperature Tc approximate to 0.032 exhibits notable differences from previous static and dynamical mean-field estimates, implying a significant role of quantum fluctuations near the onset of superconductivity in this gapless flat-band system.