Entanglement asymmetry in the gapped XYZ spin-$\frac12$ chain

Abstract

The entanglement asymmetry measures how strongly a symmetry is broken inside a subsystem. Analytic results at equilibrium have so far covered free theories and, perturbatively, the critical XXZ chain. We compute the R\'enyi entanglement asymmetries of a large interval in the gapped, $U(1)$-breaking phase of the interacting XYZ chain. The calculation combines three ingredients. A charged-moment identity, which we prove for fermionic Gaussian and for injective matrix-product ground states, ties the asymmetry to the static susceptibility of the broken charge. A non-conservation sum rule then evaluates the susceptibility from sine-Gordon form factors, its two-kink and one-breather channels providing a lower bound on the universal amplitude. The Baxter--Johnson--Krinsky--McCoy solution supplies the kink mass for different couplings. Infinite-system density-matrix renormalization group simulations built on these masses reproduce the master formula.