Ground-state-energy universality of noninteracting fermionic systems

When noninteracting fermions are confined in a D-dimensional region of volume 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.

Automated summary

The ground-state energy of noninteracting fermions confined in a D-dimensional region is not dependent on the potential V under certain conditions. This universality property holds for various scenarios, including bounded and unbounded states, and extends to thermal states. Furthermore, it draws an interesting analogy between Anderson's orthogonality catastrophe and first-order quantum phase transitions.