Negativity spectrum in 1D gapped phases of matter

Abstract

We investigate the spectrum of the partial transpose (negativity spectrum) of two adjacent regions in gapped one-dimensional models. We show that, in the limit of large regions, the negativity spectrum is entirely reconstructed from the entanglement spectrum of the bipartite system. We exploit this result in the XXZ spin chain, for which the entanglement spectrum is known by means of the corner transfer matrix. We find that the negativity spectrum levels are equally spaced, the spacing being half that in the entanglement spectrum. Moreover, the degeneracy of the spectrum is described by elegant combinatorial formulas, which are related to the counting of integer partitions. We also derive the asymptotic distribution of the negativity spectrum. We provide exact results for the logarithmic negativity and for the moments of the partial transpose. They exhibit unusual scaling corrections in the limit $\Delta \to 1^{+}$ with a corrections exponent which is the same as that for the Rényi entropies.

20 pages, 7 figures. As published. Contribution to the special issue of J. Phys. A: "John Cardy's scale-invariant journey in low dimensions: a special issue for his 70th birthday"

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• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
• Symmetry decomposition of negativity of massless free fermions
• Twisted and untwisted negativity spectrum of free fermions
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Singularity in Entanglement Negativity Across Finite Temperature Phase Transitions
• Finite-temperature entanglement negativity of free fermions
• Entanglement negativity spectrum of random mixed states: A diagrammatic approach
• Negativity spectrum in 1D gapped phases of matter
• The Negativity Hamiltonian: An operator characterization of mixed-state entanglement
• Negativity Spectrum in the Random Singlet Phase
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Stochastic Adaptive Single-Site Time-Dependent Variational Principle
• Negativity Spectra in Random Tensor Networks and Holography
• Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case
• Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain
• Entanglement and classical fluctuations at finite-temperature critical points
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Quantum information spreading in random spin chains
• Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
• Scale Invariant Entanglement Negativity at the Many-Body Localization Transition
• Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
• Quench dynamics of Rényi negativities and the quasiparticle picture
• Non-local Order Parameters and Quantum Entanglement for Fermionic Topological Field Theories
• Symmetry protected entanglement in random mixed states
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Quench dynamics of negativity Hamiltonians
• Probing phase transitions in non-Hermitian systems with quantum entanglement