Details

Autor(en) / Beteiligte

• Jones, Nick G.

Titel

Symmetry-Resolved Entanglement Entropy in Critical Free-Fermion Chains

Ist Teil von

• Journal of statistical physics, 2022-09, Vol.188 (3), Article 28

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2022

Quelle

SpringerNature Journals

Beschreibungen/Notizen

• The symmetry-resolved Rényi entanglement entropy is the Rényi entanglement entropy of each symmetry sector of a density matrix ρ . This experimentally relevant quantity is known to have rich theoretical connections to conformal field theory (CFT). For a family of critical free-fermion chains, we present a rigorous lattice-based derivation of its scaling properties using the theory of Toeplitz determinants. We consider a class of critical quantum chains with a microscopic U(1) symmetry; each chain has a low energy description given by N massless Dirac fermions. For the density matrix, ρ A , of subsystems of L neighbouring sites we calculate the leading terms in the large L asymptotic expansion of the symmetry-resolved Rényi entanglement entropies. This follows from a large L expansion of the charged moments of ρ A ; we derive tr ( e i α Q A ρ A n ) = a e i α ⟨ Q A ⟩ ( σ L ) - x ( 1 + O ( L - μ ) ) , where a ,  x and μ are universal and σ depends only on the N Fermi momenta. We show that the exponent x corresponds to the expectation from CFT analysis. The error term O ( L - μ ) is consistent with but weaker than the field theory prediction O ( L - 2 μ ) . However, using further results and conjectures for the relevant Toeplitz determinant, we find excellent agreement with the expansion over CFT operators.