Strong coupling expansion for the Bose-Hubbard and the Jaynes-Cummings lattice model

Abstract

A strong coupling expansion, based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et al. [Phys. Rev. B 79, 195131] and Teichmann et al. [Phys. Rev. B 79, 224515] is implemented in order to study various aspects of the Bose-Hubbard and the Jaynes-Cummings lattice model. The approach, which allows to generate numerically all diagrams up to a desired order in the interaction strength is generalized for disordered systems and for the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and the Jaynes-Cummings lattice model will be presented and compared with results from VCA and DMRG. Our focus will be on the Mott insulator to superfluid transition.

29 pages, 21 figures

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Cited by in corpus (9)

• Beyond hard-core bosons in transmon arrays
• High-order symbolic strong-coupling expansion for the Bose-Hubbard model
• Hypergeometric continuation of divergent perturbation series. I. Critical exponents of the Bose-Hubbard model
• Perturbative calculation of critical exponents for the Bose-Hubbard model
• Hypergeometric analytic continuation of the strong-coupling perturbation series for the 2d Bose-Hubbard model
• Quantum critical properties of Bose-Hubbard models
• Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model
• Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems
• Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions