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  • Open Access

Operator space transport in collective spin Lindbladians

Dominik Nemeth*, Ahsan Nazir, Robert-Jan Slager, and Alessandro Principi

  • *Contact author: dominik.nemeth@manchester.ac.uk
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Phys. Rev. B 114, 214305 – Published 14 October, 2026

DOI: https://doi.org/10.1103/x51f-y16f

Abstract

Boundary time crystals (BTCs) are paradigmatic examples of continuous time crystals that emerge in collective, dissipative quantum systems. Their microscopic origin, however, remains obscured by the complexity of Lindbladian many-body dynamics and has largely been investigated through semiclassical and numerical approaches. Here, we develop an exact operator space framework for collective spin Lindbladians based on irreducible tensor representations. We map the Lindbladian dynamics onto a local non-Hermitian hopping problem, where weak symmetries impose selection rules on operator transport, while the hopping amplitudes and their relative strengths determine the resulting dynamical regimes. We identify the microscopic ingredients that distinguish models supporting conventional collective precession from those supporting BTC dynamics. Our approach further reveals how nonunital dissipation can provide a source for the traceless operator subspace, revealing a microscopic mechanism for the reduced sensitivity of BTC dynamics to initial conditions beyond mean-field descriptions. More broadly, our results establish operator space transport as a general perspective for understanding dissipative many-body dynamics and its connections to non-Hermitian phenomena.

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Phys. Rev. B 114, 214305– Published 14 October, 2026
  • Received 4 June 2026
  • Revised 4 September 2026
  • Accepted 21 September 2026
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