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arXiv:2309.16523 · New Journal of Physics

Time crystal embodies chimeralike state in periodically driven quantum spin system

Mahbub Rahaman, Akitada Sakurai, Analabha Roy

Published Jun 1, 2024• 2 citations
arXivHTMLPDF

Abstract

Abstract Chimera states are a captivating occurrence in which a system composed of multiple interconnected elements exhibits a distinctive combination of synchronized and desynchronized behavior. The emergence of these states can be attributed to the complex interdependence between quantum entanglement and the delicate balance of interactions among system constituents. The emergence of discrete-time crystal (DTC) in typical many-body periodically driven systems occurs when there is a breaking of time translation symmetry. Coexisting coupled DTC and a ferromagnetic dynamically many-body localized (DMBL) phase at distinct regions have been investigated under the controlled spin rotational error of a disorder-free spin-1/2 chain for different types of spin-spin interactions. We contribute a novel approach for the emergence of the DTC-DMBL-chimeralike state, which is robust against external static fields in a periodically driven quantum many-body system.

DOI
10.1088/1367-2630/ad5757

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Abstract Chimera states are a captivating occurrence in which a system composed of multiple interconnected elements exhibits a distinctive combination of synchronized and desynchronized behavior. The emergence of these states can be attributed to the complex interdependence between quantum entanglement and the delicate balance of interactions among system constituents. The emergence of discrete-time crystal (DTC) in typical many-body periodically driven systems occurs when there is a breaking of time translation symmetry. Coexisting coupled DTC and a ferromagnetic dynamically many-body localized (DMBL) phase at distinct regions have been investigated under the controlled spin rotational error of a disorder-free spin-1/2 chain for different types of spin-spin interactions. We contribute a novel approach for the emergence of the DTC-DMBL-chimeralike state, which is robust against external static fields in a periodically driven quantum many-body system.
Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of matter appear in a variety of quantum technology applications. Such symmetries are normally broken in spatial dimension, however, they can also be broken temporally leading to the concept of discrete time symmetries and their associated crystals. Discrete time crystals (DTCs) are a novel state of matter emerging in periodically driven quantum systems. Typically, they have been investigated assuming individual control operations with uniform rotation errors across the entire system. In this work we explore a new paradigm arising from nonuniform rotation errors, where two dramatically different phases of matter coexist in well defined regions of space. We consider a quantum spin network possessing long-range interactions where different driving operations act on different regions of that network. What results from its inherent symmetries is a system where one region is a DTC, while the second is ferromagnetic. We envision our work to open a new avenue of research on chimeralike phases of matter where two different phases coexist in space.
We investigate the dynamical phases that emerge in collective spin models subjected to a spatially non-uniform periodic drive. Taking the paradigmatic Lipkin-Meshkov-Glick (LMG) model as a concrete platform, we establish that a rich landscape of dynamical phases emerges when two regions of the system are driven with different field strengths, h1h_1h1​ and h2h_2h2​. Remarkably, despite the `all-to-all' nature of the interactions, the system can be driven into dynamical phases characterized by distinct kinds of discrete time crystal (DTC) orders in different parts of the system. Apart from these coexisting DTCs, tuning the driving field leads to the emergence of phases where DTCs coexist with Floquet-synchronized or oscillatory phases; the former has been dubbed a chimera DTC. Finally, we demonstrate that a tunable set of global DTC phases emerges when h1h_1h1​ and h2h_2h2​ are proximate. Crucially, these dynamical regimes can be observed both for experimentally relevant finite-size systems and in the thermodynamic limit. Our results establish spatially structured driving as a powerful route to realize non-equilibrium phase coexistence in collective spin systems.
Discrete time crystals (DTC) have emerged as a significant phase of matter for out-of-equilibrium many-body systems. In this work, we study how random long-range interactions contribute to the stability of the DTC phase. Generally, a stable DTC phase is believed to be realized in disordered systems with short-range interactions. Here, we explore a periodically driven quantum Sherrington-Kirkpatrick (SK) model of Ising spin-glass in which all spins are coupled to each other randomly. We investigate the possibilities of the DTC phase in the SK model within three different driving protocols and found that the quantum SK model exhibits a robust DTC phase, although systems with uniform long-range interactions can exhibit only prethermal DTC phase. Further, we demonstrate that disorder in the local XYXYXY term or transverse field is crucial for stabilizing a broad DTC phase, despite random couplings in the SK model. Our analysis shows that the stability of the DTC phase is determined by the non-ergodic nature of the Floquet eigenstates.
The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.
Discrete time crystals (DTCs) are phases of matter characterized by the presence of an observable evolving with nTnTnT periodicity under a TTT-periodic Hamiltonian, where n>1n>1n>1 is an integer insensitive to small parameter variations. In particular, DTCs with n=2n=2n=2 have been extensively studied in periodically quenched and kicked spin systems in recent years. In this paper, we study the emergence of DTCs in a many-body system whose semiclassical mean-field dynamics is nonintegrable, using a rather simple model depicting a harmonically driven spin chain. We advocate to first employ a semiclassical approximation to arrive at a mean-field Hamiltonian and then identify the parameter regime at which DTCs exist, with standard tools borrowed from studies of classical chaos. Specifically, we seek symmetric-breaking solutions by examining the stable islands on the Poincar\'e surface of section of the mean-field Hamiltonian. We then turn to the actual many-body quantum system, evaluate the stroboscopic dynamics of the total magnetization in the full quantum limit, and verify the existence of DTCs. Our effective and straightforward approach indicates that in general DTCs are one natural aspect of many-body quantum chaos with mixed classical phase space structure. Our approach can also be applied to general time-periodic systems, which is thus promising for finding DTCs with n>2n>2n>2 and opening possibilities for exploring DTCs properties beyond their time-translational breaking features.
We investigate the non-equilibrium dynamics of a Heisenberg spin-1/2 chain driven by a periodic magnetic field. Based on its instantaneous integrability and inherent symmetry, we analytically study the magnetization and many-body tunneling (MBT). Both of them exhibit periodicity distinct from the driving period. The magnetization is shown to be independent of the initial state and robust against perturbations, signaling the formation of discrete time crystal (DTC) order. The DTC phase is found to be continuously tunable through magnetic field. The system exhibits perfect MBT, manifested as exactly vanishing Loschmidt echo (LE) thus divergent LE rate function at half period of the DTC. Remarkably, the perfect MBT is independent of the system size, and can be traced to an effective gap closure induced by quantum geometric effects. Furthermore, the Loschmidt echo spectra entropy shows logarithmic-dependence on system size, consistent with non-thermal nature of the DTC phase. We propose a protocol using ultracold atoms for experimental realization of the DTC and MBT.