Variational Cluster Perturbation Theory for Bose-Hubbard models

Abstract

We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator--to--superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum -- free of spurious gaps -- despite the fact that if formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimension dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed.

v1) 10 pages, 6 figures. v2) Final version as published

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• Characterization of Mott-insulating and superfluid phases in the one-dimensional Bose--Hubbard model
• Non-perturbative renormalization-group approach to the Bose-Hubbard model
• Multiband bosons in optical lattices
• Spectral properties of the square-lattice antiferromagnetic J1-J2 Heisenberg model: confinement and deconfinement of spinons
• Application of a multi-site mean-field theory to the disordered Bose-Hubbard model
• Spectral properties of strongly correlated bosons in two-dimensional optical lattices
• Self-energy-functional theory for systems of interacting electrons with disorder
• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase
• Spectral properties of coupled cavity arrays in one dimension
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• Polariton Mott insulator with trapped ions or circuit QED
• Nonequilibrium self-energy functional theory
• Quantum phase transition and excitations of the Tavis-Cummings lattice model
• Extended self-energy functional approach for strongly-correlated lattice bosons in the superfluid phase
• Benchmarking the variational cluster approach by means of the one-dimensional Bose-Hubbard model
• Bosonic self-energy functional theory
• Variational cluster approach to the single impurity Anderson model
• Excitations in disordered bosonic optical lattices
• Phase diagram reconstruction of the Bose-Hubbard model with a Restricted Boltzmann Machine wavefunction
• Capturing the re-entrant behaviour of one-dimensional Bose-Hubbard model
• Variational Cluster Approximation to the Thermodynamics of Quantum Spin Systems
• Quantum cluster approach to the topological invariants in correlated Chern insulators
• Optical Response in Excitonic Insulating State: Variational Cluster Approach
• Polaritonic properties of the Jaynes-Cummings lattice model in two dimensions
• Self-energy functional theory with symmetry breaking for disordered lattice bosons
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model
• Finite temperature phase diagram of the extended Bose-Hubbard model in the presence of disorder