Entanglement and particle correlations of Fermi gases in harmonic traps

Abstract

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx π^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.

15 pages, 22 figs

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Cited by in corpus (40)

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• Dynamics of Charge-Resolved Entanglement after a Local Quench
• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Coherent and dissipative dynamics at quantum phase transitions
• Phase transitions and edge scaling of number variance in Gaussian random matrices
• Finite temperature free fermions and the Kardar-Parisi-Zhang equation at finite time
• Random matrices and entanglement entropy of trapped Fermi gases
• Stationary entanglement entropies following an interaction quench in 1D Bose gas
• Entanglement Entropy and Full Counting Statistics for $2d$-Rotating Trapped Fermions
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Point Processes with Gaussian Boson Sampling
• Universal ground state properties of free fermions in a $d$-dimensional trap
• Number statistics for $\beta$-ensembles of random matrices: applications to trapped fermions at zero temperature
• Quantum dynamics and entanglement of a 1D Fermi gas released from a trap
• Counting statistics for non-interacting fermions in a $d$-dimensional potential
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Full counting statistics for interacting trapped fermions
• Surface and bulk entanglement in free-fermion chains
• Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit
• Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitions
• Free fermions and the classical compact groups
• Counting statistics for non-interacting fermions in a rotating trap
• Universal covariance formula for linear statistics on random matrices
• Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap
• Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap
• Kinetic energy of a trapped Fermi gas at finite temperature
• Equilibrium and nonequilibrium entanglement properties of 2D and 3D Fermi gases
• Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps
• Free fermions and $\alpha$-determinantal processes
• Entanglement in composite free-fermion systems
• Correlations vs connectivity in R-charge
• Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature
• Information measures for a local quantum phase transition: Lattice bosons in a one-dimensional harmonic trap
• Entanglement of Free Fermions and Bosons at Finite Temperature
• Numerical continuum tensor networks in two dimensions
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality