Ground-state-energy universality of noninteracting fermionic systems

TL;DR

This paper proves that for large noninteracting fermionic systems in D dimensions, the ground state energy becomes independent of the confining potential under certain conditions, revealing a universality property that extends to thermal states.

Contribution

The paper provides a proof of ground-state-energy universality for radially symmetric potentials in D dimensions, broadening understanding of energy independence in large fermionic systems.

Findings

Ground state energy is independent of potential V in the thermodynamic limit.

Universality extends to thermal states and potentials with mild conditions.

An analogy between Anderson's orthogonality catastrophe and quantum phase transitions is established.

Abstract

When noninteracting fermions are confined in a $D$-dimensional region of volume $\mathrm{O}(L^D)$ and subjected to a continuous (or piecewise continuous) potential $V$ which decays sufficiently fast with distance, in the thermodynamic limit, the ground state energy of the system does not depend on $V$. Here, we discuss this theorem from several perspectives and derive a proof for radially symmetric potentials valid in $D$ dimensions. We find that this universality property holds under a quite mild condition on $V$, with or without bounded states, and extends to thermal states. Moreover, it leads to an interesting analogy between Anderson's orthogonality catastrophe and first-order quantum phase transitions.