The Hubbard model with smooth boundary conditions

TL;DR

This paper demonstrates that smooth boundary conditions improve the efficiency of quantum Monte Carlo simulations of the 2D Hubbard model, enabling better exploration of low-temperature and doped regimes, and suggests possible d-wave superconductivity.

Contribution

It introduces the application of smooth boundary conditions to Hubbard model simulations, reducing finite-size effects and alleviating the sign problem away from half-filling.

Findings

Faster convergence to the thermodynamic limit at half-filling.

Lower temperature simulations possible away from half-filling.

Evidence of enhanced d-wave pairing correlations at certain doping and temperature.

Abstract

We apply recently developed smooth boundary conditions to the quantum Monte Carlo simulation of the two-dimensional Hubbard model. At half-filling, where there is no sign problem, we show that the thermodynamic limit is reached more rapidly with smooth rather than with periodic or open boundary conditions. Away from half-filling, where ordinarily the simulation cannot be carried out at low temperatures due to the existence of the sign problem, we show that smooth boundary conditions allow us to reach significantly lower temperatures. We examine pairing correlation functions away from half-filling in order to determine the possible existence of a superconducting state. On a $10\times 10$ lattice for $U=4$, at a filling of $\langle n \rangle = 0.87$ and an inverse temperature of $\beta=10$, we did find enhancement of the $d$-wave correlations with respect to the non-interacting case, a possible sign of $d$-wave superconductivity.