Critical scaling of the renormalized single-particle wave function near the Mott-Hubbard transition

TL;DR

This paper investigates the quantum critical behavior of the renormalized single-particle wave function near the Mott-Hubbard transition, revealing scaling laws and the influence of Coulomb repulsion in cubic lattices.

Contribution

It introduces a new analysis of the wave function scaling near the insulator-metal transition using the Gutzwiller approach, connecting it to the Mott criterion.

Findings

Wave function size scales as R^n near transition

System energy and wave function maximum follow similar scaling laws

Results agree with exact solutions for the Hubbard chain

Abstract

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 $R^{n}$. Such scaling is interpreted as the evidence of a dominant role of the Coulomb repulsion. Relation of the insulator-metal transition lattice-parameter value $R=R_{C}$ to the original {\em Mott criterion\} is obtained. The method is tested by comparing our results with the exact approach for the Hubbard chain.