We present a quantum critical behavior of the renormalized single-particle Wannier function, calculated in the Gutzwiller correlated state near the insulator-metal transition (IMT) for cubic lattices. The wave function size and its maximum, as well as the system energy scale with increasing lattice parameter
R as
Rn. Such scaling is interpreted as the evidence of a dominant role of the Coulomb repulsion. Relation of the insulator-metal transition lattice-parameter value
R=RC to the original {\em Mott criterion\} is obtained. The method is tested by comparing our results with the exact approach for the Hubbard chain.
A new mean field theory is proposed for the Mott transition in the Hubbard model based on the slave rotor representation of the electron operator. This theory provides a better description of the role of the long range charge correlation in the Mott insulating state and offers a good estimation of the critical correlation strength for the Mott transition. We have constructed a new variational wave function for the Mott insulating state based on this new slave rotor mean field theory. We find this new variational wave function outperforms the conventional Jastrow type wave function with long range charge correlator in the Mott insulating state. It predicts a continuous Mott transition with non-divergent quasiparticle mass at the transition point. We also show that the commonly used on-site mean field decoupling for the slave rotor corresponds to the Gutzwiller approximation for the Gutzwiller projected wave function with only on-site charge correlator, which can not describe the Mott transition in any finite dimensional system.
The Tomonaga-Luttinger parameter K ρ determines the critical behavior in quasi–one-dimensional correlated electron systems, e.g. , the exponent α for the density of states near the Fermi energy. We use the numerical density-matrix renormalization group method to calculate K ρ from the slope of the density-density correlation function in momentum space at zero wave vector. We check the accuracy of our new approach against exact results for the Hubbard and XXZ Heisenberg models. We determine K ρ in the phase diagram of the extended Hubbard model at quarter filling, n c = 1/2, and confirm the bosonization results K ρ = n c 2 = 1/4 on the critical line and K ρ CDW = n c 2 /2 = 1/8 at infinitesimal doping of the charge-density-wave (CDW) insulator for all interaction strengths. The doped CDW insulator exhibits exponents α > 1 only for small doping and strong correlations.