Quantum criticality around metal-insulator transitions of strongly correlated electrons

TL;DR

This paper explores an unconventional quantum criticality at metal-insulator transitions in correlated electrons, revealing a new universality class with unique critical behavior that challenges traditional symmetry-breaking frameworks.

Contribution

It demonstrates that Hartree-Fock approximations can capture this novel criticality, connecting microscopic models with experimental observations and extending the understanding of quantum phase transitions.

Findings

Identification of an unconventional universality class at metal-insulator transitions.

Critical exponents remain robust beyond mean-field approximations.

Experimental data supports the existence of marginal quantum criticality.

Abstract

Quantum criticality of metal-insulator transitions in correlated electron systems is shownto belong to an unconventional universality class with violation of Ginzburg-Landau-Wilson(GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square latticesare capable of such metal-insulator transitions with unusual criticality under a preexisting symmetry breaking. The obtained universality is consistent with the scaling theory formulated for Mott transition and with a number of numerical results beyond the mean-field level, implying that the preexisting symmetry breaking is not necessarily required for the emergence of this unconventional universality. Examinations of fluctuation effects indicate that the obtained critical exponents remain essentially exact beyond the mean-field level. Detailed analyses on the criticality, containing diverging carrier density fluctuations around the marginal quantum critical point, are presented from microscopic calculations and reveal the nature as quantum critical "opalescence". Analyses on crossovers between GLW type at nonzero temperature and topological type at zero temperature show that the critical exponents observed in (V,Cr)2O3 and kappa-ET-type organic conductor provide us with evidences for the existence of the present marginal quantum criticality.