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 (25)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• 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 phases in an optical lattice
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• The spectral weight of the Hubbard model through cluster perturbation theory
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Phases of the one-dimensional Bose-Hubbard model
• Self-energy-functional approach to systems of correlated electrons
• Variational cluster approach to correlated electron systems in low dimensions
• Cluster Perturbation Theory for Hubbard models
• Dynamics and Thermodynamics of the Bose-Hubbard model
• Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
• Antiferromagnetic to superconducting phase transition in the hole- and electron-doped Hubbard model at zero temperature
• 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
• Mott transition in one dimension: Benchmarking dynamical cluster approaches
• The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study
• Variational Cluster Perturbation Theory for Bose-Hubbard models
• Spectral properties of strongly correlated bosons in two-dimensional optical lattices
• Spectral properties of coupled cavity arrays in one dimension

Cited by in corpus (11)

• Characterization of Mott-insulating and superfluid phases in the one-dimensional Bose--Hubbard model
• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase
• Spectral properties and phase diagram of correlated lattice bosons in an optical cavity within the B-DMFT
• Beyond the Hubbard bands in strongly correlated lattice bosons
• Variational cluster approach to the single impurity Anderson model
• Numerical calculation of spectral functions of the Bose-Hubbard model using B-DMFT
• Strong coupling expansion for the Bose-Hubbard and the Jaynes-Cummings lattice model
• Excitations in disordered bosonic optical lattices
• Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium
• Two-particle Correlation Functions in Cluster Perturbation Theory: Hubbard Spin Susceptibilities
• Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion