Temperature Derivative of the Superfluid Density in the Attractive Hubbard model

TL;DR

This paper uses advanced Quantum Monte-Carlo simulations to identify the Kosterlitz-Thouless transition in the attractive Hubbard model by analyzing the temperature derivative of the superfluid density, revealing size-dependent responses away from half-filling.

Contribution

It introduces a numerical method to detect the transition by calculating the temperature derivative of superfluid density in the Hubbard model.

Findings

Confirmed the Kosterlitz-Thouless transition via numerical data.

Observed size-dependent response of the derivative away from half-filling.

No such response observed at half-band filling.

Abstract

Based on extensions of the grand-canonical Quantum Monte-Carlo algorithm to incorporate magnetic fields, we provide numerical data confirming the existence of a Kosterlitz-Thouless transition in the attractive Hubbard model. Here, we calculate the temperature derivative of the superfluid density, to pin down the transition. Away from half-band filling, the above quantity, shows a response which increases with lattice size at the transition temperature. In contrast, such a signal is not observed for the case of a half-band filling.