Universality class of quantum criticality in the two-dimensional Hubbard model at intermediate temperatures ($t^2/U\ll T\ll t$)

TL;DR

This paper demonstrates that the quantum critical behavior of the two-dimensional Hubbard model at intermediate temperatures aligns with the dilute Fermi gas universality class, with universal observables accurately described by weakly interacting fermions.

Contribution

It establishes the dilute Fermi gas as the correct universality class for the Mott/metal crossover in the 2D Hubbard model at intermediate temperatures, supported by numerical evidence.

Findings

Density and compressibility are universal functions of chemical potential.

No scaling collapse observed for kinetic energy, double occupancy, and spin correlations.

Magnetic field introduces physics beyond the dilute Fermi gas universality class.

Abstract

We show that the dilute Fermi gas quantum critical universality class quantitatively describes the Mott/metal crossover of the two-dimensional Hubbard model for temperatures somewhat less than (roughly half) the tunneling but much greater than (roughly twice) the superexchange energy. We calculate the observables expected to be universal near the transition --- density and compressibility --- with numerically exact determinantal quantum Monte Carlo. We find they are universal functions of the chemical potential. Despite arising from the strongly correlated regime of the Hubbard model, these functions are given by the weakly interacting, dilute Fermi gas model. These observables and their derivatives are the only expected universal static observables of this universality class, which we also confirm by verifying there is no scaling collapse of the kinetic energy, fraction of doubly occupied sites, and nearest neighbor spin correlations. Our work resolves the universality class of the intermediate temperature Mott/metal crossover, which had alternatively been proposed to be described by more exotic theories. However, in the presence of a Zeeman magnetic field, we find that interplay of spin with itinerant charge can lead to physics beyond the dilute Fermi gas universality class.