Work

Hierarchical Time Crystals

Year: 2026

Type: article

Abstract: Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or continuous. While these distinct types of time crystals have been extensively explored as stand-alone systems, intriguing effects can arise from their mutual interaction. Here, we demonstrate that a time-independent coupled system of discrete and continuous time crystals induces a simultaneous twofold temporal symmetry breaking, resulting in a hierarchical time crystal phase. Interestingly, one of the subsystems breaks a discrete temporal symmetry that is absent from the time-independent Liouvillian generating the dynamics, but instead emerges dynamically, giving rise to a convoluted nonequilibrium phase. We demonstrate that hierarchical time crystals are robust, emerging for fundamentally different coupling schemes and persisting across wide ranges of system parameters.

Source: Physical Review Letters

DOI: 10.1103/7mv6-4g91

Authors: Jan Carlo Schumann, Igor Lesanovsky, Parvinder Solanki

Institutions: University of Tübingen, University of Nottingham, Indian Institute of Space Science and Technology

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green