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  • Open Access

Spontaneous breaking of a continuous symmetry at a nonconformal quantum critical point in one dimension

R. Flores-Calderón1,2,*,† and M. Zündel3,4,*,‡

  • *These authors contributed equally to this work.
  • †Contact author: r.flores-calderon@tum.de
  • ‡Contact author: martina.zuendel@uibk.ac.at
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Phys. Rev. Research 8, 043001 – Published 1 October, 2026

DOI: https://doi.org/10.1103/yhpf-7451

Abstract

In this work, we present numerical evidence for the spontaneous breaking of a continuous U(1) symmetry in a nearest-neighbor interacting spin-1 chain at a quantum critical point separating two XY quasi-long-range ordered phases distinguished by a spontaneously broken Z2 symmetry. Remarkably, the continuous symmetry breaking emerges precisely at the critical point of the discrete order parameter, suggesting a mechanism beyond currently established scenarios. At criticality, the XY correlations develop true long-range order, accompanied by a finite perpendicular magnetization, a zero-frequency Bragg peak in the transverse dynamical structure factor, and sharp gapless collective excitations. From complementary static and dynamical observables, we quantitatively determine the critical exponents, obtaining a dynamical exponent z=1.50±0.04 and an anomalous dimension η=1.04±0.03. Remarkably, the value of z coincides with the one-dimensional Kardar-Parisi-Zhang exponent despite the system being an equilibrium quantum many-body system. We further show that the noninteracting continuum limit is equivalent to the recently introduced transverse quantum fluid, displaying their off-diagonal long-ranged order in one dimension. Complementing the numerical study, we derive the renormalization-group flow equations of the continuum theory to second order in the ɛ expansion. We identify an interacting fixed point whose critical behavior differs from the Ising universality class already at two-loop order, although the perturbative exponents remain far from the numerical values.

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Phys. Rev. Research 8, 043001– Published 1 October, 2026
  • Received 22 January 2026
  • Revised 13 July 2026
  • Accepted 5 September 2026
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