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arXiv:2608.28126

Self-partitioned Interfacial Time Crystals

Joseph Huang, Yi Yang

physics.opticscond-mat.mes-hallphysics.atom-phquant-phSubmitted Aug 28, 2026• Announced Aug 31, 2026• 0 citations
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Abstract

Nonequilibrium many-body systems can spontaneously break symmetry in time, as in time crystals, or in space, through self-organized domains and interfaces. Whether these two forms of symmetry breaking can intertwine so that an emergent interface alone hosts time-crystalline order remains unknown. In this work, by introducing the Rabi-Hatano-Nelson model, we unveil the existence and mechanism of a self-partitioned interfacial time crystal (SPITC), where a homogeneous system generates its own internal and tunable interface, at which the time-translation symmetry is also spontaneously broken. Such a SPITC phase is intrinsically induced by nonreciprocity and open boundary conditions, without external pumping or long-range interaction. The periodic and open boundary phase diagrams of the system are both mapped out; vacuum and Dicke-like superradiance with static or active orders are identified, with analytical phase boundaries in the weak coupling limit. The frequency of the SPITC is found to scale quadratically with the spin-photon coupling strength, as we derive analytically for the slow dynamics of the spins. The position of the SPITC boundary scales with a critical exponent of $-1$ as a function of the degree of nonreciprocity, in stark contrast to $-1/2$ for an otherwise stationary boundary. Our construction of SPITC establishes a route to spatiotemporal order in non-Hermitian many-body systems.

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Nonequilibrium many-body systems can spontaneously break symmetry in time, as in time crystals, or in space, through self-organized domains and interfaces. Whether these two forms of symmetry breaking can intertwine so that an emergent interface alone hosts time-crystalline order remains unknown. In this work, by introducing the Rabi-Hatano-Nelson model, we unveil the existence and mechanism of a self-partitioned interfacial time crystal (SPITC), where a homogeneous system generates its own internal and tunable interface, at which the time-translation symmetry is also spontaneously broken. Such a SPITC phase is intrinsically induced by nonreciprocity and open boundary conditions, without external pumping or long-range interaction. The periodic and open boundary phase diagrams of the system are both mapped out; vacuum and Dicke-like superradiance with static or active orders are identified, with analytical phase boundaries in the weak coupling limit. The frequency of the SPITC is found to scale quadratically with the spin-photon coupling strength, as we derive analytically for the slow dynamics of the spins. The position of the SPITC boundary scales with a critical exponent of −1-1−1 as a function of the degree of nonreciprocity, in stark contrast to −1/2-1/2−1/2 for an otherwise stationary boundary. Our construction of SPITC establishes a route to spatiotemporal order in non-Hermitian many-body systems.
The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of nonstationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred to as time crystals, and they can be realized, for example, in many-body systems governed by collective dissipation and long-ranged interactions. Here, we provide a complete analytical characterization of a boundary time-crystal phase transition. This involves exact expressions for the order parameter and for the dynamics of quantum fluctuations, which, in the time-crystalline phase, remains asymptotically non-Markovian as a consequence of the time-translation symmetry breaking. We demonstrate that boundary time crystals are intrinsically critical phases, where fluctuations exhibit a power-law divergence with time. Our results show that a dissipative time-crystal phase is far more than merely a classical nonlinear and nonstationary (limit cycle) dynamics of a macroscopic order parameter. It is rather a genuine many-body phase where the properties of correlations distinctly differ from those of stationary ones.
Time crystals are systems that spontaneously break time-translation symmetry, exhibiting repeating patterns in time. Recent work has shown that non-Hermitian Floquet systems can host a time crystalline phase with quasi-long-range order. In this work, we investigate the effect of introducing a non-integrable interaction term into this non-Hermitian time crystal model. Using a combination of numerical TEBD simulations, mean-field analysis, and perturbation theory, we find that the interaction term has two notable effects. First, it induces a shift in the phase diagram, moving the boundaries between different phases. Second, a sufficiently strong interaction induces an unexpected symmetry-breaking transition, which is not captured by the mean-field approach. Within average Hamiltonian theory, we trace this back to a ferromagnetic transition in the anisotropic non-Hermitian XXZ model. Our results demonstrate that the interplay between non-Hermitian dynamics and many-body interactions can lead to novel symmetry breaking.
Discrete time crystals (DTCs) exhibit a special nonequilibrium phase of matter in periodically driven many-body systems with spontaneous breaking of time translational symmetry. The presence of decoherence generally enhances thermalization and destroys the coherence required for the existence of DTCs. In this paper, we devise a mechanism for establishing a stable DTC with period-doubling oscillations in an open quantum system that is governed by a properly tailored non-Hermitian Hamiltonian. We find a specific class of nonreciprocal couplings in our non-Hermitian dynamics which prevents thermalization through eigenstate ordering. This choice of non-Hermitian dynamics significantly enhances the stability of the DTC against imperfect pulses. Through a comprehensive analysis, we determine the phase diagram of the system in terms of pulse imperfection.
Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time-translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in various driven-dissipative quantum platforms. The current understanding of CTCs is mainly based on mean-field theories, which fail to address the problem of whether the continuous time-translation symmetry can be broken in noisy, spatially extended systems absent in all-to-all couplings. Here, we propose a CTC realized in a quantum contact model through self-organized bistability. The CTCs stem from the interplay between collective dissipation induced by the first-order absorbing phase transitions and slow constant driving provided by an incoherent pump. The stability of such oscillatory phases in finite dimensions under the action of intrinsic quantum fluctuations is scrutinized by the functional renormalization group method and numerical simulations. Occurring at the edge of many-body synchronization, the CTC phase exhibits an inherent period and amplitude with a coherence time linearly diverging with system size, thus also constituting a boundary time crystal. Our results serve as a solid route towards self-protected CTCs in strongly interacting open systems. Published by the American Physical Society 2024
Nonequilibrium driving systems provide fertile ground for exploring intriguing spontaneous symmetry breaking phenomena. In this paper, we report on the intertwined discrete spacetime translational symmetry breaking in a driven-dissipative spin system without pure spatial translational symmetry, resulting in the emergence of an out-of-equilibrium nonmagnetic phase termed the ``discrete spacetime crystal.'' In contrast to the previously widely studied discrete time crystal, the spins establish a distinctive long-range crystalline order not only in time, but also in the intertwined spacetime direction. We further demonstrate the exponentially long lifetime of the spatial-temporal order against generic weak environmental noise fluctuations. Finally, possible experimental realizations of our model are discussed. Our findings shed light on the existence of exotic phases of matter characterized by intertwined spacetime symmetry breaking, paving the way for future investigations into the properties and potential applications of these exotic states.
Time crystals are many-body states that spontaneously break translation symmetry in time the way that ordinary crystals do in space. While experimental observations have confirmed the existence of discrete or continuous time crystals, these realizations have relied on the utilization of periodic forces or effective modulation through cavity feedback. The original proposal for time crystals is that they would represent self-sustained motions without any external periodicity, but realizing such purely self-generated behavior has not yet been achieved. Here, we provide theoretical and experimental evidence that many-body interactions can give rise to an inherent time crystalline phase. Following a calculation that shows an ensemble of pumped four-level atoms can spontaneously break continuous time translation symmetry, we observe periodic motions in an erbium-doped solid. The inherent time crystal produced by our experiment is self-protected by many-body interactions and has a measured coherence time beyond that of individual erbium ions.