Entanglement spectrum in one-dimensional systems

2008/06/30 by Pasquale Calabrese, Alexandre Lefèvre, Alexandre Lefevre · 6 citations
Mathematics · Physics and Astronomy · #Block (permutation group theory) #Central charge #Combinatorics #Conformal field theory #Conformal map #Eigenvalues and eigenvectors #Field (mathematics) #Function (biology) #Geometry #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Scaling #Spectrum (functional analysis) #Statistical physics #cond-mat.stat-mech #cond-mat.str-el #hep-th #quant-ph

paper · pdf · doi:10.1103/physreva.78.032329

published as Phys. Rev A 78, 032329 (2008) · 4 pages, 3 figures, typos corrected, Refs added

openalex publication_date 2008/09/23 · arxiv created 2008/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We derive the distribution of eigenvalues of the reduced density matrix of a block of length \ensuremathℓ in a one-dimensional system in the scaling regime. The resulting ``entanglement spectrum'' is described by a universal scaling function depending only on the central charge of the underlying conformal field theory. This prediction is checked against exact results for the XX chain. We also show how the entanglement gap closes when \ensuremathℓ is large.

Citations

• On single-copy entanglement
• Renyi entropy of the XY spin chain
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Calculation of reduced density matrices from correlation functions
• Density-matrix spectra of solvable fermionic systems
• Scaling of entanglement support for matrix product states
• Entanglement in many-body systems
• Half the entanglement in critical systems is distillable from a single specimen

Cited by

• Entanglement negativity after a global quantum quench
• Critical behavior of the two-dimensional icosahedron model
• Holographic phases of Rényi entropies
• Entanglement and Majorana edge states in the Kitaev model
• Entanglement between particle partitions in itinerant many-particle states
• Finite temperature entanglement negativity in conformal field theory