Ground-state-energy universality of noninteracting fermionic systems
| Autor: | Silva, Douglas F. C. A., Ostilli, Massimo, Presilla, Carlo |
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| Rok vydání: | 2021 |
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| Zdroj: | Phys. Rev. A 104, 023309 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.104.023309 |
| Popis: | 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. Comment: 9 pages |
| Databáze: | arXiv |
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