Symmetry-resolved entanglement entropy in critical free-fermion chains

Nick G. Jones

doi:10.1007/s10955-022-02941-3

paper

Symmetry-resolved entanglement entropy in critical free-fermion chains

arXiv:2202.11728 · doi:10.1007/s10955-022-02941-3

Abstract

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 $t r (e^{i α Q_{A}} ρ_{A}^{n}) = a e^{i α ⟨ Q_{A} ⟩} (σ L)^{- x} (1 + O (L^{- μ}))$ , 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.

20 pages + appendix

Symmetry-resolved entanglement entropy in critical free-fermion chains

Abstract

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