The charge spin-separation, pseudogap formation and phase diagrams are studied in two and four site Hubbard clusters using analytical diagonalization and grand canonical ensemble method in a multidimensional parameter space of temperature, magnetic field, on-site Coulomb interaction (
U≥0), and chemical potential. The numerically evaluated, exact expressions for charge and spin susceptibilities provide clear evidence for the existence of true gaps in the ground state and pseudogaps in a limited range of temperature. In particular, Mott-Hubbard type charge crossover, spin pseudogap and magnetic correlations with antiferromagnetic (spin) pseudogap structure for two and four site clusters closely resemble the pseudogap phenomena and the normal-state phase diagram in high T
c superconductors. ~ ~
Abstract Cluster mean field theory for the two-dimensional spin-1 Bose–Hubbard model is applied to study superfluid (SF) to Mott insulator (MI) phase transitions and various magnetic phases that arise in the presence of spin-dependent anti-ferromagnetic and ferromagnetic interactions. This study clearly shows the nematic behavior of SF and odd-density MI phases, and a continuous phase transition between them for anti-ferromagnetic interaction. The even-density MI shows a nematic or singlet phase depending upon the strength of the interaction, and a continuous crossover between them. The SF to singlet MI transition is discontinuous. The dependence of cluster size on the critical on-site interaction ( U 0 C ) for SF to MI transitions is also studied. In the case of anti-ferromagnetic interaction, it is found that U 0 C for the SF to odd-density MI transition decreases with cluster size; however, no such changes are observed for the SF to singlet MI transition. In the case of ferromagnetic interactions, SF to MI transitions are continuous, and Mott lobes become enlarged with cluster size. Second order Rényi entanglement entropy (EE) is calculated in different phases. The results show that Rényi EE is large in the nematic MI phase.
We investigate the temperature-dependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a two-dimensional optical lattice, described by the Bose-Hubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster mean-field theory (CMF) where the effect of non-local correlations is analyzed systematically by finite-size scaling of the cluster size. The phase diagram exhibits a rich structure including a transition and a crossover of the SF and MI phases respectively to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finite-size scaling agree quantitatively with quantum Monte Carlo (QMC) results as well as with experiments. The von Neumann entanglement entropy of a cluster exhibits critical enhancement near the SF-MI quantum critical point (QCP). We also discuss the behavior of the transition lines near this QCP at the particle-hole symmetric point located at the tip of a Mott lobe as well as away from particle-hole symmetry.