The Cluster Mean Field theory calculation is extended for finite temperatures to study the combined effect of quantum and thermal fluctuations on various phases arising in the spin-1 Bose Hubbard model. This investigation finds that the polar nature of the superfluid phase persists, and the density of bosons with spin component σ = 0 increases with the temperature. The phase diagram is obtained and compared with that of the single-site mean-field theory. Compressibility shows a signature of divergence at the transition from the polar superfluid phase to the normal bose liquid phase. Small thermal fluctuations are sufficient to destroy the anti-ferromagnetic, maximally entangled odd density Mott insulator phase, whereas large thermal fluctuations are needed to break the singlet formed in the even density Mott insulator phase. However, in both the cases, the insulators melt to normal bose liquid at the same temperature.
Abstract The properties of a recently discovered unrestricted Hartree‐Fock solution of the Hubbard Hamiltonian is analysed on the square lattice that shows a really two‐dimensional spin polarization of a vortex‐like character. This and other several mean‐field solutions are compared with the exact ground‐state energy and wave function of two and four electrons on a four‐site system (square). Results for two correlated electrons in large 3 × 3 and 4 × 4 clusters are also given and discussed. The vortex mean‐field solution provides the best solution in almost all systems that deviate from half‐filling.
We present results for the equation of state of the two-dimensional Hubbard model on an isotropic square lattice as obtained from a controlled and numerically exact large-cluster dynamical mean field simulation. Our results are obtained for large but finite systems and are extrapolated to infinite system size using a known finite-size scaling relation, and are supplemented by reliable error bars accounting for all sources of errors. We establish the importance of examining the decay of spatial spin correlations to determine whether a sufficiently large cluster has been used and with this in mind we present the energy, entropy, double occupancy, and nearest-neighbor spin correlations extrapolated to the thermodynamic limit. We discuss the implications of these calculations on pseudogap physics of the 2D Hubbard model away from half filling, where we find a strong behavioral shift in energy below a temperature
T∗ which becomes more pronounced for larger clusters. Finally, we provide reference calculations and tables for the equation of state for values of doping away from half filling which are of interest to cold-atom experiments.