$\mathbb{Z}_2$ Universality of the Mott Transition

TL;DR

This paper reveals that the Mott transition's universal scaling behavior stems from a $ ext{Z}_2$ symmetry breaking in momentum space, with charge compressibility serving as the order parameter, supported by extensive numerical evidence.

Contribution

It demonstrates the $ ext{Z}_2$ universality of the Mott transition and identifies charge compressibility as the key order parameter, supported by numerical simulations and comparison with cold-atom experiments.

Findings

Charge compressibility acts as the order parameter.

Universal scaling of Widom line temperature with $U$.

Temperature of minimum second derivative scales universally.

Abstract

We demonstrate that the Mott transition exhibits universal scaling as a consequence of the breaking of a $\mathbb{Z}_2$ symmetry in momentum space. A direct consequence of this discrete symmetry breaking is the charge or Mott gap itself. From extensive numerics, we proffer that it is the charge compressibility that acts as the underlying order parameter as it is zero in the insulator and non-zero in the metallic state. Additionally, the Widom line (temperature of the extremum of the compressibility) obeys a universal scaling of $T_m=0.39U$ deep into the insulating state directly from $Z_2$ universality. Furthermore, the temperature at which the second derivative of the compressibility has a minimum is independent of lattice geometry, exhibiting a universal scaling of $|U-U_c|^\alpha$ where $\alpha\approx 1$. Finally, our computational approach reproduces the key features of the doping dependence of the compressibility demonstrated in recent cold-atom quantum simulators of the Hubbard model, thereby corroborating our conclusions on $\mathbb{Z}_2$ universality.