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

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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 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.
Original languageEnglish
Pages (from-to)235122
Number of pages1
JournalPhysical review / E
Volume81
Issue number23
DOIs
Publication statusPublished - 1 Jun 2010

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Hubbard Model
Benchmarking
reference systems
lobes
Density Matrix
boundary conditions
Parameter Space
Quantum Phase Transition
Open Boundary Conditions
Matrix Groups
Superfluid
Ground State Energy
perturbation theory
Strong Coupling
Convergence Properties
Renormalization Group
Perturbation Theory
ground state
Higher Order
Benchmark

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Benchmarking the variational cluster approach by means of the one-dimensional Bose-Hubbard model. / Knap, Michael; Arrigoni, Enrico; von der Linden, Wolfgang.

In: Physical review / E, Vol. 81, No. 23, 01.06.2010, p. 235122.

Research output: Contribution to journalArticleResearchpeer-review

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