Symmetry-resolved entanglement entropy in critical free-fermion chains

• URL: http://arxiv.org/abs/2202.11728v2
• Date: Tue, 12 Jul 2022 19:58:06 GMT
• Title: Symmetry-resolved entanglement entropy in critical free-fermion chains
• Authors: Nick G. Jones
• Abstract summary: symmetry-resolved R'enyi entanglement entropy is known to have rich theoretical connections to conformal field theory. We consider a class of critical quantum chains with a microscopic U(1) symmetry. For the density matrix, $rho_A$, of subsystems of $L$ neighbouring sites we calculate the leading terms in the large $L$ expansion of the symmetry-resolved R'enyi entanglement entropies.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The symmetry-resolved R\'enyi entanglement entropy is the R\'enyi 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 R\'enyi entanglement entropies. This follows from a large $L$ expansion of the charged moments of $\rho_A$; we derive $tr(e^{i \alpha Q_A} \rho_A^n) = a e^{i \alpha \langle Q_A\rangle} (\sigma L)^{-x}(1+O(L^{-\mu}))$, 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.

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