2020/08/31 by Naftali R. Smith, Pierre Le Doussal, Satya N. Majumdar +1 · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #cond-mat.quant-gas #math-ph #math.MP
paper · pdf · doi:10.1103/physreve.103.l030105
published as Phys. Rev. E 103, 030105 (2021) · Main text: 8 pages, 1 figure. Supplemental material: 22 pages, 6 figures
arxiv created 2021/03/18 · arxiv updated 2021/03/31
We develop a first-principle approach to compute the counting statistics in the ground-state of N noninteracting spinless fermions in a general potential in arbitrary dimensions d (central for d>1). In a confining potential, the Fermi gas is supported over a bounded domain. In d=1, for specific potentials, this system is related to standard random matrix ensembles. We study the quantum fluctuations of the number of fermions \cal N\cal D in a domain \calD of macroscopic size in the bulk of the support. We show that the variance of \cal N\cal D grows as N(d-1)/d (Ad log N + Bd) for large N, and obtain the explicit dependence of Ad, Bd on the potential and on the size of \cal D (for a spherical domain in d>1). This generalizes the free-fermion results for microscopic domains, given in d=1 by the Dyson-Mehta asymptotics from random matrix theory. This leads us to conjecture similar asymptotics for the entanglement entropy of the subsystem \calD, in any dimension, supported by exact results for d=1.