A Scaling Function for the Particle Entanglement Entropy of Fermions

Abstract

Entanglement entropy under a particle bipartition provides complementary information to mode entanglement as it is sensitive to interactions and particle statistics at leading order and does not depend on any externally imposed length scale. In this paper, we investigate the particle entanglement entropy in a system of $N$ interacting spinless lattice fermions in one spatial dimension by combining bosonization techniques with exact and approximate numerical methods. We introduce a general scaling form for the fermionic particle entanglement entropy captured by a shape function that enters as a extensive interaction induced correction to a known free fermion result. A general asymptotic expansion in the total number of particles demonstrates that its form is robust for different values of the Rényi index and highlights how quantum correlations are encoded in the $n$-particle density matrix of a pure many-body quantum state.

33 pages, 12 figures. For associated data and code repository see: https://github.com/DelMaestroGroup/papers-code-scalingParticleEE

References in corpus (21)

• The Luttinger model following a sudden interaction switch-on
• Quantum Phase Transitions and Bipartite Entanglement
• Quantum quench dynamics of the Luttinger model
• General criterion for the entanglement of two indistinguishable particles
• Entanglement entropy in fermionic Laughlin states
• Bipartite entanglement entropy in fractional quantum Hall states
• Entanglement and Particle Identity: A Unifying Approach
• Entanglement, Particle Identity and the GNS Construction: A Unifying Approach
• Entropy and Exact Matrix Product Representation of the Laughlin Wave Function
• A path integral Monte Carlo method for Rényi entanglement entropies
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• Entanglement entropy, single-particle occupation probabilities, and short-range correlations
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Particle partitioning entanglement in itinerant many-particle systems
• Particle partition entanglement of bosonic Luttinger liquids
• Particle Entanglement in Rotating Gases
• Local density of states and particle entanglement in topological quantum fluids
• Balls and Walls: A Compact Unary Coding for Bosonic States
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• Novel phases in rotating Bose-condensed gas: vortices and quantum correlation

Cited by in corpus (1)

• Matrix product states and first quantization