arXiv subjects

Dominik Nemeth

Publications and source records attributed to Dominik Nemeth.

3 recordsLinked to original sources

arXiv2026

Operator Space Transport and the Emergence of Boundary Time Crystals

Boundary time crystals (BTCs) are prominent examples of continuous time crystals in collective spin systems governed by Lindbladian evolution. To date, their analysis has mostly relied on semiclassical and numerical approaches. Here, we develop a fully quantum-compatible framework to classify collective spin dynamics and show that BTC behavior emerges from the absence of non-trivial weak symmetries of the Liouvillian. To this end, we introduce an irreducible tensor representation of operator space, in which the Lindbladian dynamics maps onto a non-Hermitian hopping problem. Within this picture, the dynamics corresponds to the transport of operator weight across tensor sectors. This mapping allows an identification of distinct dynamical regimes, including collective precession, pure relaxation, and the BTC phase, within a single unified framework. We show that BTCs arise from non-reciprocal transport in operator space, which delocalizes Liouvillian eigenmodes across multiple tensor sectors. This non-reciprocal transport provides a microscopic mechanism for the insensitivity to initial conditions of BTC oscillations. More broadly, our results establish operator space transport as a perspective for understanding dissipative many-body dynamics and highlights connections to non-Hermitian phenomena.

quant-ph↗

arXiv2026

Topological Boundary Time Crystal Oscillations

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.

quant-ph↗

arXiv2025

Analytical solution of boundary time crystals via the superspin basis

Boundary time crystals (BTCs) in dissipative collective spin systems have been extensively studied using numerical, mean-field, and perturbative approaches. However, an explicit Liouvillian description governing the long-time dynamics deep within the time crystal phase has remained elusive. Here, we derive an effective Liouvillian that analytically captures the extreme BTC regime, where dissipation is parametrically weak and oscillatory order is maximally robust. By introducing a superspin representation of Liouville space, we obtain closed-form expressions for the Liouvillian eigenvalues to first order in the dissipation strength, providing direct access to decay rates, oscillation frequencies, and their thermodynamic scaling. Applying this framework to the canonical BTC model we analytically recover spontaneous breaking of continuous time-translation symmetry and persistent oscillations in the thermodynamic limit. In contrast, we show that other dissipative spin models exhibit only single-frequency oscillatory dynamics and therefore do not support genuine BTC phases. Our results establish a controlled analytical framework for the long-time dynamics in the extreme BTC regime.

quant-ph↗