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

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.

12 pages, 16 figures, minor changes, version as published

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Quantum phase transitions of light
• The ALPS project release 1.3: open source software for strongly correlated systems
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• Variational cluster approach to correlated electron systems in low dimensions
• Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
• Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects
• Spectral weight redistribution in strongly correlated bosons in optical lattices
• Process chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram
• The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study
• Mott transition in one dimension: Benchmarking dynamical cluster approaches

Cited by in corpus (2)

• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase
• Excitations in disordered bosonic optical lattices