Strong-coupling solution of the bosonic dynamical mean-field theory

Abstract

We derive an approximate analytical solution of the self-consistency equations of the bosonic dynamical mean-field theory (B-DMFT) in the strong-coupling limit. The approach is based on a linked-cluster expansion in the hybridization function of normal bosons around the atomic limit. The solution is used to compute the phase diagram of the bosonic Hubbard model for different lattices. We compare our results with numerical solutions of the B-DMFT equations and numerically exact methods, respectively. The very good agreement with those numerical results demonstrates that our approach captures the essential physics of correlated bosons both in the Mott insulator and in the superfluid phase. Close to the transition into the superfluid phase the momentum distribution function at zero momentum is found to be strongly enhanced already in the normal phase. The linked-cluster expansion also allows us to compute dynamical properties such as the spectral function of bosons. The evolution of the spectral function across the transition from the normal to the superfluid phase is seen to be characteristically different for the interaction driven and density driven transition, respectively.

8 pages, 6 figures

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Theory of ultracold Fermi gases
• Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
• Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases
• Quantum Phase Diagram of Bosons in Optical Lattices
• Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results
• Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory
• Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory
• Effective Action Approach for Quantum Phase Transitions in Bosonic Lattices
• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase

Cited by in corpus (5)

• Nonequilibrium dynamical mean-field theory for bosonic lattice models
• Spectral properties and phase diagram of correlated lattice bosons in an optical cavity within the B-DMFT
• Numerical calculation of spectral functions of the Bose-Hubbard model using B-DMFT
• Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium
• Degenerate approach to the mean field Bose- Hubbard Hamiltonian