Analytical solution of boundary time crystals via the superspin basis

Fuente: arXiv
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Autori principali: Nemeth, Dominik, Principi, Alessandro, Nazir, Ahsan
Natura: Preprint
Pubblicazione: 2025
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author Nemeth, Dominik
Principi, Alessandro
Nazir, Ahsan
author_facet Nemeth, Dominik
Principi, Alessandro
Nazir, Ahsan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_06998
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Analytical solution of boundary time crystals via the superspin basis
Nemeth, Dominik
Principi, Alessandro
Nazir, Ahsan
Quantum Physics
Other Condensed Matter
Statistical Mechanics
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.
title Analytical solution of boundary time crystals via the superspin basis
topic Quantum Physics
Other Condensed Matter
Statistical Mechanics
url https://arxiv.org/abs/2507.06998