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Q: Fachverband Quantenoptik und Photonik

Q 9: Open Quantum Systems and Spin-Boson Systems I

Q 9.1: Talk

Monday, March 2, 2026, 17:00–17:15, P 4

Hierarchical time translational symmetry breaking — •Jan Carlo Schumann¹, Igor Lesanovsky^1,2, and Parvinder Solanki¹ — ¹Institute for Theoretical Physics, University of Tübingen, Germany — ²School of Physics and Astronomy, University of Nottingham, United Kingdom

Spontaneous symmetry breaking is one of the central organizing principles in physics. Recently, time crystals have emerged as a new phase of matter, spontaneously breaking the time translational symmetry. Depending on the nature of symmetry breaking, they are mainly categorized as discrete (DTC) or continuous (CTC) time crystals. While CTCs and DTCs have been explored independently, the potential effects emerging from their mutual interaction remain unexplored. In this work, we demonstrate that hierarchical time-translational symmetry breaking (HSB) stems from the interaction of a DTC and a CTC, which we term hierarchical time crystals. The HSB phenomenon unfolds in two steps. First, the CTC spontaneously breaks the continuous time translational symmetry of the system’s dynamical generator. The emerging time-periodicity of the CTC can then, in turn, be broken discretely by the DTC, manifesting in a sub-harmonic response to the CTC phase. Interestingly, the DTC breaks a symmetry that does not even exist for the generator of the dynamics, leading to a convoluted non-equilibrium phase of matter in time. We demonstrate that the novel HSB phenomenon is robust, emerging for fundamentally different coupling schemes and persisting across wide ranges of system parameters, thereby confirming the stable many-body phase.

Keywords: Time crystals; Phase transitions and critical phenomena; Hierarchical symmetries and their breaking; Synchronization