Entanglement entropy in Fermi gases and Anderson's orthogonality catastrophe

Abstract

We study the ground-state entanglement entropy of a subsystem of size $L$ of non-interacting fermions scattered by a potential of finite range $a$. We derive a general relation between the scattering matrix and the overlap matrix and use it to prove, that for a one-dimensional symmetric potential the von Neumann entropy, the Rényi entropies and the full counting statistics are robust against potential scattering, provided that $L/a\gg 1$. The results of numerical calculations support the validity of this conclusion for a generic potential.

arXiv comment5+2 pages, 1 figure, published version

References in corpus (23)

• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Time-dependence of correlation functions following a quantum quench
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• The entanglement entropy of one-dimensional gases
• A short review on entanglement in quantum spin systems
• Orthogonality catastrophe as a consequence of qubit embedding in an ultra-cold Fermi gas
• Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
• Universality in the full counting statistics of trapped fermions
• Exact relations between particle fluctuations and entanglement in Fermi gases
• Measuring entanglement using quantum quenches
• Entanglement entropy with interface defects
• Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
• Solution of the fermionic entanglement problem with interface defects
• Entanglement entropy with localized and extended interface defects
• Riemann-Hilbert approach to a generalized sine kernel and applications
• Orthogonality catastrophe and decoherence in a trapped-Fermion environment
• Free fermions on a line: asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics
• Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants
• Integral operators with the generalized sine-kernel on the real axis

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• Modular Hamiltonians for the massless Dirac field in the presence of a defect
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• Time evolution of entanglement negativity across a defect
• Entanglement negativity in free-fermion systems: An overlap matrix approach
• Universal fidelity near quantum and topological phase transitions in finite 1D systems
• Entanglement in composite free-fermion systems
• Effect of Single Impurity on Free Fermion Entanglement Entropy
• Entanglement of Free Fermions and Bosons at Finite Temperature
• Fermionic Partial Transpose in the Overlap Matrix Framework for Entanglement Negativity