Symmetry-Resolved Entanglement Entropy in Critical Free-Fermion Chains

The symmetry-resolved Renyi entanglement entropy is the Renyi entanglement entropy of each symmetry sector of a density matrix rho. 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, rho(A), of subsystems of L neighbouring sites we calculate the leading terms in the large L asymptotic expansion of the symmetry-resolved Renyi entanglement entropies. This follows from a large L expansion of the charged moments of rho(A); we derive tr(e(i alpha QA) rho(n)(A)) = ae(i alpha < QA >) (sigma L)(-x)(1 + O(L-mu)), where a, x and mu are universal and sigma 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-mu) is consistent with but weaker than the field theory prediction O(L-2 mu). However, using further results and conjectures for the relevant Toeplitz determinant, we find excellent agreement with the expansion over CFT operators.

Automated summary

The paper explores the scaling properties of symmetry-resolved Renyi entanglement entropy in a family of critical free-fermion chains and calculates the leading terms in the large L asymptotic expansion. The exponent x was found to correspond to the expectation from CFT analysis, showing good agreement with the expansion over CFT operators.