Bond-dependent slave-particle cluster theory based on density matrix expansion

TL;DR

This paper introduces a cluster slave-particle method based on density matrix expansion that significantly reduces computational cost while maintaining high accuracy for interacting Hubbard models on lattices.

Contribution

A novel slave-particle decomposition combined with a density matrix expansion transforms the lattice problem into overlapping clusters, enabling efficient and accurate simulations.

Findings

Achieves high accuracy for total energies and site occupancies

Reduces computational cost by two to three orders of magnitude

Matches density matrix renormalization group benchmarks

Abstract

Efficient and accurate computational methods for dealing with interacting electron problems on a lattice are of broad interest to the condensed matter community. For interacting Hubbard models, we introduce a cluster slave-particle approach that provides significant computational savings with high accuracy for total energies, site occupancies, and interaction energies. Compared to exact benchmarks using density matrix renormalization group for $d$-$p$ Hubbard models, our approach delivers accurate results using two to three orders of magnitude lower computational cost. Our method is based on a novel slave-particle decomposition with an improved description of particle hoppings, and a new density matrix expansion method where the interacting lattice slave-particle problem is then turned into a set of overlapping real-space clusters which are solved self-consistently with appropriate physical matching constraints at shared lattice sites between clusters.