Benchmarking the variational cluster approach by means of the one-dimensional Bose-Hubbard model

TL;DR

This paper evaluates the variational cluster approach applied to the one-dimensional Bose-Hubbard model, demonstrating its accuracy in predicting phase boundaries and static properties with low computational cost, and compares it with exact and perturbative methods.

Contribution

It benchmarks the variational cluster approach against exact and perturbative results for the 1D Bose-Hubbard model, highlighting improvements with extended variational parameters and boundary conditions.

Findings

Accurate phase boundary determination for the Mott insulator to superfluid transition.

Enhanced results with extended variational parameters and open boundary conditions.

Reliable static property calculations with low computational effort.

Abstract

Convergence properties of the variational cluster approach with respect to the variational parameter space, cluster size, and boundary conditions of the reference system are investigated and discussed for bosonic many-body systems. Specifically, the variational cluster approach is applied to the one-dimensional Bose-Hubbard model, which exhibits a quantum phase transition from Mott to superfluid phase. In order to benchmark the variational cluster approach, results for the phase boundary delimiting the first Mott lobe are compared with essentially exact density matrix renormalization group data. Furthermore, static quantities, such as the ground state energy and the one-particle density matrix are compared with high-order strong coupling perturbation theory results. For reference systems with open boundary conditions the variational parameter space is extended by an additional variational parameter which allows for a more uniform particle density on the reference system and thus drastically improves the results. It turns out that the variational cluster approach yields accurate results with relatively low computational effort for both spectral as well as static properties of the one-dimensional Bose-Hubbard model, even at the tip of the first Mott lobe where correlation effects are most pronounced.