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Spontaneous symmetry breaking in chiral current-carrying high-energy eigenstates

Tigran A. Sedrakyan1,2, Jun-Jun Pang1,3, Chenan Wei1,2, and Baigeng Wang3

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Phys. Rev. B 114, 055127 – Published 23 July, 2026

DOI: https://doi.org/10.1103/ld5r-jkh7

Abstract

Typical finite-energy-density eigenstates of nonintegrable systems are expected to obey the eigenstate thermalization hypothesis and to reproduce thermal local observables. In integrable systems, typical states are instead finite-entropy Bethe macrostates, or generalized Gibbs ensembles, with smooth quasiparticle occupations. Here we show that the spin-12 XXX Heisenberg chain contains an exactly solvable exception. By biasing mutually commuting conserved charges, we use the ground state of a selector Hamiltonian to construct rare eigenstates of the undeformed XXX Hamiltonian. These states are atypical, ordered, chiral, current-carrying, critical, zero-entropy Bethe macrostates at tunable XXX energy densities. They lie outside the finite-entropy manifold dominating generalized Gibbs ensembles, yet remain exact XXX eigenstates with sharp Bethe occupations, finite scalar chirality, nonthermal local observables, and gapless Luttinger-liquid correlations. A finite-interval thermodynamic Bethe ansatz reveals an asymmetric chiral Bethe sea whose zero-field limit selects an extensive spin sector through SU(2) symmetry breaking. A commuting exchange bias moves the same ordered macrostate through the full thermodynamic XXX energy band, including its Hilbert-space trace center. Finite-size DMRG and exact-diagonalization benchmarks indicate that the magnetochiral signatures persist under weak integrability breaking over prethermal time scales. The construction provides a controlled integrable realization of ETH-violating, scar-like large-deviation eigenstates and a route to ordered critical matter deep inside a many-body spectrum.

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Phys. Rev. B 114, 055127– Published 23 July, 2026
  • Received 14 December 2025
  • Revised 23 June 2026
  • Accepted 9 July 2026
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