Archive ouverte HAL – Ground-state energy of noninteracting fermions with a random energy spectrum

Hendrik SchaweAlexander K. HartmannSatya N. Majumdar 1 Grégory Schehr 1

EPL, 2018, 124 (4), pp.40005. 〈10.1209/0295-5075/124/40005〉

We derive analytically the full distribution of the ground-state energy of K non-interacting fermions in a disordered environment, modelled by a Hamiltonian whose spectrum consists of N i.i.d. random energy levels with distribution (with ε ≥ 0), in the same spirit as the “Random Energy Model”. We show that for each fixed K, the distribution P K, N (E 0) of the ground-state energy E 0 has a universal scaling form in the limit of large N. We compute this universal scaling function and show that it depends only on K and the exponent α characterizing the small ε behaviour of . We compared the analytical predictions with results from numerical simulations. For this purpose we employed a sophisticated importance-sampling algorithm that allowed us to obtain the distributions over a large range of the support down to probabilities as small as . We found asymptotically a very good agreement between analytical predictions and numerical results.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques