Breakdown of Quantum Chaos in the Staggered-Field XXZ Chain: Confinement and Meson Formation

TL;DR

This paper investigates how confinement of fractionalized excitations in the staggered-field XXZ chain leads to non-ergodic behavior and meson formation, revealing a transition from chaotic to localized spectra and providing a detailed meson spectroscopy framework.

Contribution

It offers a comprehensive analysis of confinement-induced non-ergodicity and develops a quantitative meson spectroscopy method in quantum spin chains, connecting theory with numerical results.

Findings

Transition from chaotic to non-ergodic spectra with increasing anisotropy

Banding of eigenstates by domain-wall number correlates with entanglement suppression

Quantitative agreement of low-lying spectrum with meson ladder predictions

Abstract

Confinement of fractionalized excitations can strongly restructure many-body spectra. We investigate this phenomenon in the gapped spin-$\frac{1}{2}$ XXZ chain subject to a staggered field, where spinons bind into domain-wall ``mesons'' deep in the antiferromagnetic phase. We present evidence that this non-integrable model exhibits both Hilbert space fractionalization and quantum scar formation as controlled by the anisotropy parameter $\Delta$. Exact diagonalization across symmetry-resolved sectors reveals a crossover from Gaussian-orthogonal (chaotic) level statistics at weak anisotropy $\Delta \sim 1$ to non-ergodic behavior deep in the antiferromagnetic regime $\Delta\gg 1$ through scrutinizing the adjacent gap ratios, accompanied by a striking banding of eigenstates by domain-wall number in correlation and entanglement measures. The Page-like entanglement dome characteristic of chaotic spectra gives way to suppressed, band-resolved entanglement consistent with emergent quasi-conservation of domain walls. To investigate further the formation mechanism of mesonic scar states, we carry out meson spectroscopy near the two-spinon threshold and compare with the analytic ladder predicted by Rutkevich [Phys. Rev. B 106, 134405 (2022)]. We test the theory through continuum-relative bindings, an offset-removed Airy scaling collapse, and explicit two-meson thresholds that determine the number of stable meson levels. The low-lying spectrum shows close quantitative agreement, while deviations at higher energies are consistent with finite-size and subleading corrections. These results establish a unified account of confinement-induced nonergodicity and provide a template for quantitative meson spectroscopy in quantum spin chains.