Analyzing the two-dimensional doped Hubbard model with the Worldvolume HMC method

TL;DR

This paper demonstrates the application of the Worldvolume HMC method to the doped two-dimensional Hubbard model, successfully computing physical observables where traditional methods fail due to the sign problem.

Contribution

The study extends the WV-HMC method to the doped 2D Hubbard model, enabling reliable calculations in regimes with severe sign problems.

Findings

Predicts physical observables on an 8x8 lattice at T/t=1/6.4 and U/t=8.0

Overcomes the sign problem where standard determinant QMC fails

Provides controlled statistical errors in doped Hubbard model simulations

Abstract

We apply the Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] to the two-dimensional Hubbard model, which is known to suffer from a severe sign problem when the system is doped (away from half filling). We show that the method predicts physical observables with controlled statistical errors on an $8 \times 8$ lattice at temperature $T/t = 1/6.4 \approx 0.156$ and interaction strength $U/t = 8.0$ ($t$ is the hopping amplitude), for which the standard determinant quantum Monte Carlo fails.