Towards entanglement negativity of two disjoint intervals for a one dimensional free fermion

Abstract

We study the moments of the partial transpose of the reduced density matrix of two intervals for the free massless Dirac fermion. By means of a direct calculation based on coherent state path integral, we find an analytic form for these moments in terms of the Riemann theta function. We show that the moments of arbitrary order are equal to the same quantities for the compactified boson at the self-dual point. These equalities imply the non trivial result that also the negativity of the free fermion and the self-dual boson are equal.

29 pages, 4 figures

References in corpus (27)

• Entanglement negativity in quantum field theory
• Entanglement spectrum in one-dimensional systems
• Remarks on the entanglement entropy for disconnected regions
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Finite temperature entanglement negativity in conformal field theory
• Entanglement entropy of two disjoint blocks in XY chains
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Entanglement negativity in the harmonic chain out of equilibrium
• Entanglement Entropy and Twist Fields
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• On the partial transpose of fermionic Gaussian states
• Scaling of entanglement between separated blocks in spin chains at criticality
• Comments on Entanglement Negativity in Holographic Field Theories
• Entanglement negativity and entropy in non-equilibrium conformal field theory
• Conformal Blocks and Negativity at Large Central Charge
• Thermal state entanglement in harmonic lattices
• Entanglement spectrum of random-singlet quantum critical points
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Holographic entanglement entropy for disconnected regions
• Entanglement Routers Using Macroscopic Singlets
• Twist operators in higher dimensions
• Thermal bound entanglement in macroscopic systems and area laws
• Holographic entanglement entropy: near horizon geometry and disconnected regions
• Bose-Fermi duality and entanglement entropies
• On shape dependence of holographic mutual information in AdS4
• Distillable entanglement and area laws in spin and harmonic-oscillator systems
• Entanglement of two blocks of spins in the critical Ising model

Cited by in corpus (41)

• Partial time-reversal transformation and entanglement negativity in fermionic systems
• Machine Learning Assisted Many-Body Entanglement Measurement
• Imbalance Entanglement: Symmetry Decomposition of Negativity
• The entanglement negativity in random spin chains
• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Symmetry-resolved dynamical purification in synthetic quantum matter
• Entanglement negativity bounds for fermionic Gaussian states
• Symmetry decomposition of negativity of massless free fermions
• Twisted and untwisted negativity spectrum of free fermions
• Negativity spectrum of one-dimensional conformal field theories
• Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Measuring Fermionic Entanglement: Entropy, Negativity, and Spin Structure
• Topological entanglement negativity in Chern-Simons theories
• Branch Point Twist Field Correlators in the Massive Free Boson Theory
• Entanglement entropies of minimal models from null-vectors
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Negativity Spectrum in the Random Singlet Phase
• Entanglement negativity in free-fermion systems: An overlap matrix approach
• Multi-charged moments of two intervals in conformal field theory
• Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case
• Logarithmic Negativity in Quantum Lifshitz Theories
• Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice
• Entanglement and negativity Hamiltonians for the massless Dirac field on the half line
• Universal entanglement and correlation measure in two-dimensional conformal field theories
• Entanglement, Replicas, and Thetas
• Entanglement entropy after selective measurements in quantum chains
• Charge imbalance resolved Rényi negativity for free compact boson: Two disjoint interval case
• Symmetry-resolved entanglement in fermionic systems with dissipation
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations
• Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
• Multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals
• Quench dynamics of Rényi negativities and the quasiparticle picture
• Entanglement in Lifshitz Fermion Theories
• The operator algebra of cyclic orbifolds
• Quench dynamics of negativity Hamiltonians
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• A contour for the entanglement negativity of bosonic Gaussian states