Quantum Mott Transition and Multi-Furcating Criticality

TL;DR

This paper presents a phenomenological theory of the quantum Mott transition, highlighting how criticality near the transition leads to multi-furcating fixed points, inhomogeneous structures, and complex competing instabilities in strongly correlated systems.

Contribution

It introduces the concept of multi-furcating criticality in quantum Mott transitions, extending beyond traditional multicriticality and explaining diverse phenomena in correlated materials.

Findings

Quantum critical points generate multiple unstable fixed points.

Inhomogeneous structures with flat dispersion points emerge near the transition.

Charge, magnetic, and superconducting instabilities compete under critical charge fluctuations.

Abstract

Phenomenological theory of the Mott transition is presented. When the critical temperature of the Mott transition is much higher than the quantum degeneracy temperature, the transition is essentially described by the Ising universality class. Below the critical temperature, phase separation or first-order transition occurs. However, if the critical point is involved in the Fermi degeneracy region, a marginal quantum critical point appears at zero temperature. The originally single Mott critical point generates subsequent many unstable fixed points through various Fermi surface instabilities induced by the Mott criticality characterized by the diverging charge susceptibility or doublon susceptibility. This occurs in marginal quantum-critical region. Charge, magnetic and superconducting instabilitites compete severely under these critical charge fluctuations. The quantum Mott transition triggers multi-furcating criticality, which goes beyond the conventional concept of multicriticality in quantum phase transitions. Near the quantum Mott transition, the criticality generically drives growth of inhomogeneous structure in the momentum space with singular points of flat dispersion on the Fermi surface. The singular points determine the quantum dynamics of the Mott transition by the dynamical exponent $z=4$. We argue that many of filling-control Mott transitions are classified to this category. Recent numerical results as well as experimental results on strongly correlated systems including transition metal oxides, organic materials and $^3$He layer adsorbed on a substrate are consistently analyzed especially in two-dimensional systems.