Diagrammatic Monte Carlo procedure for the spin-charge transformed Hubbard model

TL;DR

This paper introduces a diagrammatic Monte Carlo method based on a spin-charge transformed dual representation for the Hubbard model, enabling efficient simulations of strongly correlated systems and showing excellent agreement with existing methods.

Contribution

The paper develops a novel diagrammatic Monte Carlo algorithm using spin-charge transformation, improving efficiency in simulating strongly correlated lattice fermion models.

Findings

Accurate calculation of the filling factor at infinite onsite repulsion.

Excellent agreement with Numerical Linked Cluster Expansion data.

Rapid convergence of the diagrammatic series in the tested regime.

Abstract

Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionisation of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems. This scheme allows eliminating large expansion parameters, as well as large corrections to the density matrix that generally prevent diagrammatic methods from being efficient in this regime. As an example, I compute the filling factor for the Hubbard model at infinite onsite repulsion and compare the results to controllable data obtained from Numerical Linked Cluster Expansion. I find excellent agreement between the two methods, as well as rapid convergence of the diagrammatic series. I also report results for the momentum distribution and kinetic energy of the electrons.