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

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.81.235122· OSTI ID:21386742

Knap, Michael; Arrigoni, Enrico; Linden, Wolfgang von der ^[1]

---

1. Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz (Austria)

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 the phase boundary as well as the static properties of the one-dimensional Bose-Hubbard model, even at the tip of the first Mott lobe where correlation effects are most pronounced.

• OSTI ID: 21386742
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 81, Issue 23; Other Information: DOI: 10.1103/PhysRevB.81.235122; (c) 2010 The American Physical Society; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BENCHMARKS
BOUNDARY CONDITIONS
CONVERGENCE
CORRELATIONS
DENSITY
DENSITY MATRIX
GROUND STATES
HUBBARD MODEL
ONE-DIMENSIONAL CALCULATIONS
PERTURBATION THEORY
PHASE TRANSFORMATIONS
RENORMALIZATION
STRONG-COUPLING MODEL
SUPERFLUIDITY
VARIATIONAL METHODS
CALCULATION METHODS
CRYSTAL MODELS
ENERGY LEVELS
MATHEMATICAL MODELS
MATRICES
PARTICLE MODELS
PHYSICAL PROPERTIES