On the universality class of the Mott transition in two dimensions

TL;DR

This study uses advanced numerical methods to determine that the Mott transition in a two-dimensional Hubbard model belongs to the 2D Ising universality class, revealing critical behavior at the metal-insulator transition.

Contribution

It provides the first numerical evidence that the 2D Mott transition falls into the 2D Ising universality class, clarifying long-standing theoretical debates.

Findings

Critical exponent of correlation length ν ≈ 1.0

Mott transition belongs to the 2D Ising universality class

Finite interaction induces a genuine metal-insulator transition

Abstract

We use the two-step density-matrix renormalization group method to elucidate the long-standing issue of the universality class of the Mott transition in the Hubbard model in two dimensions. We studied a spatially anisotropic two-dimensional Hubbard model with a non-perfectly nested Fermi surface at half-filling. We find that unlike the pure one-dimensional case where there is no metallic phase, the quasi one-dimensional modeldisplays a genuine metal-insulator transition at a finite value of the interaction. The critical exponent of the correlation length is found to be $\nu \approx 1.0$. This implies that the fermionic Mott transition, belongs to the universality class of the 2D Ising model. The Mott insulator is the 'ordered' phase whose order parameter is given by the density of singly occupied sites minus that of holes and doubly occupied sites.