`Triviality' of universal relations for disordered systems

TL;DR

This paper investigates the impact of quenched disorder on universal relations in spin-1/2 fermion systems with contact interactions, revealing that disorder affects the large-momentum tail and energy relations, especially in two and three dimensions.

Contribution

It demonstrates that disorder modifies universal relations like Tan's energy relation and introduces a scale anomaly in certain dimensions.

Findings

Disorder alters the large-momentum tail of particle distribution.

Universal energy relations are affected by disorder, showing scale anomalies.

The study extends understanding of disordered fermion systems in multiple dimensions.

Abstract

The universal relations for spin-$1/2$ fermions with contact interaction in the presence of quenched disorder are discussed. The disorder is modeled by a random external potential with the Gaussian distribution and $\delta$-like two-point correlation function. Utilizing simple scaling arguments, the renormalizability of the theory, and the Hellmann-Feynman theorem we identified the large-momentum tail of particle distribution and analog of Tan's energy relation for many-fermion systems with disorder in arbitrary dimension $d\ge 2$. It is shown that the energy-pressure relation manifests a kind of scale anomaly in two and three dimensions.