Thermodynamic properties, magnetism and Mott–Hubbard-like transitions in nanoscale clusters

Abstract The charge–spin response thermodynamics in the presence of a magnetic field are calculated using analytical diagonalization of small clusters. Rigorous criteria for the Mott–Hubbard, Neel and zero-field (spin) weak pseudogap singularities ( crossovers ) in the thermodynamic charge and spin density of states are found for the first time in the exactly solvable two- and four-site Hubbard ( U ⩾ 0 ) clusters. These exact calculations of the chemical potential, magnetization, charge and spin susceptibilities show the presence of true Mott–Hubbard (charge), antiferromagnetic (spin) and zero-field (spin) ground state gaps and pseudogaps that develop at infinitesimal temperatures. These pseudogaps exist in a limited range of temperature or/and doping levels and disappear at the critical temperatures of crossovers ( bifurcations ), reminiscent of the pseudogaps and normal-state phase diagram in the high T c cuprates.