Symmetry-resolved entanglement entropy in critical free-fermion chains

DOI10.1007/S10955-022-02941-3zbMATH Open1496.82003arXiv2202.11728OpenAlexW4284973250MaRDI QIDQ2156379

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Publication date: 18 July 2022

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Abstract: The symmetry-resolved R'enyi entanglement entropy is the R'enyi entanglement entropy of each symmetry sector of a density matrix $ho$. 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, $h{o}_A$, 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 $h{o}_A$; we derive $tr(e^{ialpha{Q}_A}h{o}_A^n)=a{e}^{ialphalangle{Q}_{A}angle}(sigmaL{)}^{-x}(1+O(L^{-mu}))$, 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 $O(L^{-2mu})$. However, using further results and conjectures for the relevant Toeplitz determinant, we find excellent agreement with the expansion over CFT operators.

Full work available at URL: https://arxiv.org/abs/2202.11728

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