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

Abstract

We introduce a cluster slave-particle theory for Hubbard models based on a density matrix expansion approach over overlapping real-space clusters. We improve on prior slave-particle approaches by extending the description of the slave operators to correctly describe particle hopping along bonds between sites in the system. The interacting lattice slave-particle problem is then turned into a set of overlapping real-space clusters which are solved self-consistently and with appropriate physical matching constraints at shared lattice sites between clusters. Our cluster expansion approach leads to an exact description for short-ranged correlations with the cluster radius and joins that smoothly to an approximated description of long-ranged correlations. Specifically, it avoids making large errors caused by cutting bonds at cluster boundaries. We test our theory in 1D and 2D d-p Hubbard model and compare it to exact ground-state benchmark results. Our method reproduces accurate total energies, site occupancies, and double occupancies with modest computational costs.