Process chain approach to high-order perturbation calculus for quantum lattice models

TL;DR

This paper introduces a high-order perturbation method for quantum lattice models that efficiently computes ground-state properties across various geometries and large on-site state spaces, demonstrated on the Bose-Hubbard model.

Contribution

It develops a process chain approach based on Rayleigh-Schroedinger perturbation theory for high-order series expansions in quantum lattice models.

Findings

Accurately computed the zero-temperature phase diagram of the Bose-Hubbard model.

Applicable to large spatial dimensions and large on-site state spaces.

Validated on hypercubic lattices with various fillings.

Abstract

A method based on Rayleigh-Schroedinger perturbation theory is developed that allows to obtain high-order series expansions for ground-state properties of quantum lattice models. The approach is capable of treating both lattice geometries of large spatial dimensionalities d and on-site degrees of freedom with large state space dimensionalities. It has recently been used to accurately compute the zero-temperature phase diagram of the Bose-Hubbard model on a hypercubic lattice, up to arbitrary large filling and for d=2, 3 and greater [Teichmann et al., Phys. Rev. B 79, 100503(R) (2009)].