Abstract
We develop a quantum many-body theory of the Bose-Hubbard model based on the canonical quantization of the action derived from a Gutzwiller mean-field ansatz. Our theory is a systematic generalization of the Bogoliubov theory of weakly-interacting gases. The control parameter of the theory, defined as the zero point fluctuations on top of the Gutzwiller mean-field state, remains small in all regimes. The approach provides accurate results throughout the whole phase diagram, from the weakly to the strongly interacting superfluid and into the Mott insulating phase. As specific examples of application, we study the two-point correlation functions, the superfluid stiffness, the density fluctuations, for which quantitative agreement with available quantum Monte Carlo data is found. In particular, the two different universality classes of the superfluid-insulator quantum phase transition at integer and non-integer filling are recovered.
Highlights
The Hubbard model is one of the most celebrated models of quantum condensed matter theory
The rich physics of the strongly interacting BH model across the Mott-superfluid transition and in the insulating phase has been attacked through a number of different approaches, ranging from semianalytical methods such as random phase approximation (RPA) [21,22,23], slaveboson representation [24,25], and time-dependent Gutzwiller approximation [26,27] to numerical techniques including quantum Monte Carlo methods [28,29,30,31], bosonic dynamical mean-field theory (B-DMFT) [32,33,34], and numerical renormalization group (NRG) [35,36]
We have introduced a simple and powerful semianalytical tool to study the many-body physics of quantum interacting particles on a lattice based on a canonical quantization of the fluctuations around the Gutzwiller ground state
Summary
The Hubbard model is one of the most celebrated models of quantum condensed matter theory. The rich physics of the strongly interacting BH model across the Mott-superfluid transition and in the insulating phase has been attacked through a number of different approaches, ranging from semianalytical methods such as random phase approximation (RPA) [21,22,23], slaveboson representation [24,25], and time-dependent Gutzwiller approximation [26,27] to numerical techniques including quantum Monte Carlo methods [28,29,30,31], bosonic dynamical mean-field theory (B-DMFT) [32,33,34], and numerical renormalization group (NRG) [35,36]. IV with an outlook on future studies and on possible extensions of the quantum formalism introduced in this work
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