Emergent quantum algebras in dissipative time crystals
Abstract
Strong dynamical symmetries provide an algebraic description of persistent oscillations in open quantum systems governed by the Lindblad equation. For finite-dimensional systems with a full-rank stationary state, such symmetries are necessary and sufficient for non-decaying oscillatory modes to appear in the Liouvillian's spectrum. These modes can be directly constructed by acting on stationary states with the identified symmetry operators. Here we establish an asymptotic counterpart of this algebra for collective spins. Taking a single spin S in a magnetic field, subject to dissipation through linear jump operators, we identify the exact conditions on the field and dissipative couplings under which non-decaying oscillatory modes emerge as S → ∞. We then write down a simple, closed form for the corresponding `symmetry' operator which can be applied to the steady state to construct these modes, which are eigenvectors of the Liouvillian, with imaginary eigenvalues, up to O(1/S) corrections. A second operator, an emergent conserved quantity, completes the algebra, and its slow relaxation determines how quantum noise selects the stationary state. The construction can be directly extended to a pair of interacting spins sharing a common reservoir, with the resulting quantum algebra making the entanglement during a quench analytically accessible.
Related
- Quantum Hamiltonian time crystals from covariant quantum Landau--Lifshitz--Gilbert relaxation
- Locality-Preparation Time Tradeoffs in Dissipative Quantum Systems
- Time Crystals on Quantum Devices
- Emergent Wigner magnon crystals in a fully frustrated Heisenberg four-leg tube
- Real-space Visualization of Emergent Electron Crystals in Rhombohedral Graphene
BibTeX
@misc{tindall2026emergent,
title = {{Emergent quantum algebras in dissipative time crystals}},
author = {Joseph Tindall},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16609},
eprint = {2610.16609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16609},
}
RIS
TY - UNPB
TI - Emergent quantum algebras in dissipative time crystals
AU - Joseph Tindall
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16609
UR - https://arxiv.org/abs/2610.16609
AB - Strong dynamical symmetries provide an algebraic description of persistent oscillations in open quantum systems governed by the Lindblad equation. For finite-dimensional systems with a full-rank stationary state, such symmetries are necessary and sufficient for non-decaying oscillatory modes to appear in the Liouvillian's spectrum. These modes can be directly constructed by acting on stationary states with the identified symmetry operators. Here we establish an asymptotic counterpart of this algebra for collective spins. Taking a single spin S in a magnetic field, subject to dissipation through linear jump operators, we identify the exact conditions on the field and dissipative couplings under which non-decaying oscillatory modes emerge as S → ∞. We then write down a simple, closed form for the corresponding `symmetry' operator which can be applied to the steady state to construct these modes, which are eigenvectors of the Liouvillian, with imaginary eigenvalues, up to O(1/S) corrections. A second operator, an emergent conserved quantity, completes the algebra, and its slow relaxation determines how quantum noise selects the stationary state. The construction can be directly extended to a pair of interacting spins sharing a common reservoir, with the resulting quantum algebra making the entanglement during a quench analytically accessible.
ER -