Entanglement spectrum and Rényi entropies of nonrelativistic conformal fermions

Abstract

We characterize non-perturbatively the Rényi entropies of degree n = 2, 3, 4, and 5 of threedimensional, strongly coupled many-fermion systems in the scale-invariant regime of short interaction range and large scattering length, i.e. in the unitary limit. We carry out our calculations using lattice methods devised recently by us. Our results show the effect of strong pairing correlations on the entanglement entropy, which modify the sub-leading behavior for large subsystem sizes (as characterized by the dimensionless parameter x = kF LA, where kF is the Fermi momentum and LA the linear subsystem size), but leave the leading order unchanged relative to the non-interacting case. Moreover, we find that the onset of the sub-leading asymptotic regime is at surprisingly small x 2 − 4. We provide further insight into the entanglement properties of this system by analyzing the spectrum of the entanglement Hamiltonian of the two-body problem from weak to strong coupling. The low-lying entanglement spectrum displays clear features as the strength of the coupling is varied, such as eigenvalue crossing and merging, a sharp change in the Schmidt gap, and scale invariance at unitarity. Beyond the low-lying component, the spectrum appears as a quasi-continuum distribution, for which we present a statistical characterization; we find, in particular, that the mean shifts to infinity as the coupling is turned off, which indicates that that part of the spectrum represents non-perturbative contributions to the entanglement Hamiltonian. In contrast, the low-lying entanglement spectrum evolves to finite values in the noninteracting limit. The scale invariance of the unitary regime guarantees that our results are universal features intrinsic to three-dimensional quantum mechanics and represent a well-defined prediction for ultracold atom experiments, which were recently shown to have direct access to the entanglement entropy.

Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices and particle-partition entanglement

“…7, we present our results for S α as a function of α for fixed particle numbers N = 3 + 3, 5 + 5, 7 + 7 at γ = 2.0 and fixed partition n = 1. As in calculations of spatial entanglement in higher dimensions [49], we find that the large-α limit of S α is reached rather quickly, as the variation between α = 2 and α = 5 is within 5% of the value at α = 2 for every case we explored. In fact, we observe an exponential decay of the form…”

Particle partition entanglement of one dimensional spinless fermions

“…2 (b)). A careful finite-size analysis of this unexpected feature (due to the lack of any natural length scale describing the partition) would require moving beyond exact diagonalization and employing recently adapted hybrid Monte Carlo methods [37,47,48].…”

Entanglement entropies and fermion signs of critical metals

“…The (fermion) sign problem is just in the way of explicitly enumerating the ground states of sign-full systems, and these have been entirely ignored. These should exhibit a longer-range entanglement entropy, the simple case in point being the Fermi gas with its area-log-area scaling [46]. Given the sensitivity of the bipartite entanglement entropies to the presence of signs, the next question to ask is whether the bipartite entropies are sensitive to any special features in the sign structure.…”