Random matrices and entanglement entropy of trapped Fermi gases

Abstract

We exploit and clarify the use of random matrix theory for the calculation of the entanglement entropy of free Fermi gases. We apply this method to obtain analytic predictions for Renyi entanglement entropies of a one-dimensional gas trapped by a harmonic potential in all the relevant scaling regimes. We confirm our findings with accurate numerical calculations obtained by means of an ingenious discretisation of the reduced correlation matrix.

12 pages, 6 figures, one subsection added in v2

References in corpus (23)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement negativity in quantum field theory
• Entanglement spectrum in one-dimensional systems
• Quantum Noise as an Entanglement Meter
• Scaling of entanglement support for Matrix Product States
• Entanglement of low-energy excitations in Conformal Field Theory
• Full counting statistics in a propagating quantum front and random matrix spectra
• Entanglement Entropy in the O(N) model
• Entanglement from Charge Statistics: Exact Relations for Many-Body Systems
• The entanglement entropy of one-dimensional gases
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Unusual Corrections to Scaling in Entanglement Entropy
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Phase transitions and edge scaling of number variance in Gaussian random matrices
• Towards measuring Entanglement Entropies in Many Body Systems
• Universal behavior of the Shannon and Rényi mutual information of quantum critical chains
• Free fermions on a line: asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics
• Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitions
• Equilibrium and nonequilibrium entanglement properties of 2D and 3D Fermi gases
• Entanglement entropy in Fermi gases and Anderson's orthogonality catastrophe

Cited by in corpus (26)

• Entanglement equipartition in critical random spin chains
• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• More on the rainbow chain: entanglement, space-time geometry and thermal states
• Counting statistics for non-interacting fermions in a $d$-dimensional potential
• Free fermions at the edge of interacting systems
• Full counting statistics for interacting trapped fermions
• From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies
• Generating Entanglement by Quantum Resetting
• Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap
• Rényi entropy and negativity for massless Dirac fermions at conformal interfaces and junctions
• Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects
• Dynamical phase transition in the occupation fraction statistics for non-crossing Brownian particles
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• Wigner function for noninteracting fermions in hard wall potentials
• Noninteracting particles in a harmonic trap with a stochastically driven center
• Finiteness of Entanglement Entropy in Collective Field Theory
• Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature
• Stationary time correlations for fermions after a quench in the presence of an impurity
• Measuring full counting statistics in a trapped-ion quantum simulator
• Full counting statistics of 1d short-range Riesz gases in confinement
• Spatio-temporal fluctuations in the passive and active Riesz gas on the circle
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• PhD thesis "Extreme value statistics of strongly correlated systems: fermions, random matrices and random walks"