`Triviality' of universal relations for disordered systems

V. Pastukhov

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arXiv · 2409.01271

`Triviality' of universal relations for disordered systems

V. Pastukhov

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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.

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V. Pastukhov. 2024-09-02. `Triviality' of universal relations for disordered systems. https://arxiv.org/abs/2409.01271

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