Stochastic series expansion simulation of the $t$-$V$ model

TL;DR

This paper introduces an efficient quantum Monte Carlo algorithm combining stochastic series expansion and determinantal techniques to simulate the half-filled spinless $t$-$V$ model, enabling detailed phase diagram mapping.

Contribution

The authors develop a novel algorithm that improves simulation efficiency for the $t$-$V$ model on bipartite lattices, reducing computational complexity and eliminating time-discretization errors.

Findings

Mapped the finite temperature phase diagram of the $t$-$V$ model on honeycomb lattices.

Observed suppression of the charge density wave critical temperature near a quantum critical point.

Demonstrated linear scaling with inverse temperature and cubic with system size.

Abstract

We present an algorithm for the efficient simulation of the half-filled spinless $t$-$V$ model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size and is free from the time-discretization error. We use it to map out the finite temperature phase diagram of the spinless $t$-$V$ model on the honeycomb lattice and observe a suppression of the critical temperature of the charge density wave phase in the vicinity of a fermionic quantum critical point.