Topological Boundary Time Crystal Oscillations

• URL: http://arxiv.org/abs/2602.17765v1
• Date: Thu, 19 Feb 2026 19:00:17 GMT
• Title: Topological Boundary Time Crystal Oscillations
• Authors: Dominik Nemeth, Ahsan Nazir, Alessandro Principi, Robert-Jan Slager,
• Abstract summary: Boundary time crystals (BTCs) break time-translation symmetry and exhibit long-lived, robust oscillations insensitive to initial conditions.<n>We show that collective spin BTCs can admit emergent topological winding numbers in operator space.<n>Our results frame BTC dynamics as a form of topologically constrained operator space transport.
• Score: 39.146761527401424
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Boundary time crystals (BTCs) break time-translation symmetry and exhibit long-lived, robust oscillations insensitive to initial conditions. We show that collective spin BTCs can admit emergent topological winding numbers in operator space. Expanding the density operator in a spherical tensor basis, we map the Lindblad dynamics onto an effective local hopping problem, where collective degrees of freedom label sites of an emergent two-dimensional operator space lattice and identify topological obstructions that enforce the delocalization of operator modes on the lattice. The resulting spectral delocalization provides a natural explanation for the robust oscillatory dynamics observed in BTCs. When combined with non-reciprocal transport of operator weight across operator space, this mechanism moreover also leads to the universality of long-time dynamics across a broad class of initial states. Our results frame BTC dynamics as a form of topologically constrained operator space transport and suggest a close connection to non-Hermitian skin-effects.

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