Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2302.08056 · Physical review. B./Physical review. B

Analytical theory of cat scars with discrete time-crystalline dynamics in Floquet systems

Biao Huang

Published Sep 12, 2023• 14 citations
arXivHTMLPDF

Abstract

We reconstruct the spectral pairing theories to enable analytical descriptions of eigenstate spatiotemporal orders in translation-invariant system without prethermal conditions. It is shown that the strong Ising interactions and drivings alone stabilize a class of ``cat scar'' eigenstates with tunable patterns, which lead to local discrete time-crystal (DTC) dynamics. They exhibit Fock space localization and long-range correlations robust against generic perturbations in a disorder-free scenario. In particular, we introduce a symmetry indicator method to enumerate cat scars, with which a set of unexpected inhomogeneous scar patterns are identified in addition to the ferromagnetic scars found before. These scars enforce DTC dynamics with rigid inhomogeneous patterns, offering a viable way to verify underlying eigenstate properties experimentally. Further, we prove rigorously that the strong Ising interactions enforces a selection rule for perturbations of different orders, which imposes an exponential suppression of spin fluctuations for Floquet eigenstates. Based on this property, three analytical scaling relations are proved to characterize the amplitudes, Fock space localization, and lifetime for DTC dynamics associated with cat scars. We further provide two practical methods to check whether certain DTC phenomena are dominated by single-spin dynamics or due to genuine interaction effects.

DOI
10.1103/physrevb.108.104309

Related papers

Discrete Time Crystals Enforced by Floquet-Bloch Scars

Biao Huang, Tsz-Him Leung, Dan Stamper-Kurn +1 more

We analytically identify a new class of quantum scars protected by spatiotemporal translation symmetries, dubbed Floquet-Bloch scars. They are distinguished from previous (quasi-)static scars by a rigid spectral pairing only possible in Floquet systems, where strong interaction and drivings equalize the quasienergy corrections to all scars and maintain their spectral spacings against generic bilinear perturbations. Scars then enforce the spatial localization and rigid discrete time crystal (DTC) oscillations as verified numerically in a trimerized kagome lattice model relevant to recent cold atom experiments. Our analytical solutions offer a potential scheme to understand the mechanisms for more generic translation-invariant DTCs.

arXiv:2205.07919•Physical Review Letters•Sep 19, 2022•24 citations

Analytical quantification of strongly disordered discrete time crystals

Anonymous, Biao Huang

Discrete time crystals (DTCs) have emerged as a novel non-equilibrium phenomenon. Nevertheless, analytical quantification for disordered DTCs remains challenging, leaving uncertainties about their behaviors in large scale systems amid current debates on the stability of (Floquet-)many-body localization. In this work, we introduce an analytical framework to calculate the values of key observables in a strongly disordered DTC without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement with numerical simulations for inverse participation ratios for eigenstate localization in Fock space, Edwards-Anderson parameters for spin-glass orders, mutual information for long-range entanglement, and the steady-state amplitudes of autocorrelators for period-doubled oscillations. Meanwhile, we demonstrate that eigenstate resonances render the scaling for the deviation of physical observables from their unperturbed values as $O(λ)$, in contrast to non-resonant situations with suppressed deviation $O(λ^2)$. Our newly developed scheme adopts resolvent perturbation formalism, which can directly prescribe arbitrarily higher-order corrections without iterations. With such advantages, we analytically prove that quasienergy corrections for pairwise cat eigenstates are identical up to order $O(λ^{(L/n_{\text{op}})-1})$, where perturbations of strength $λ$ involve at most $n_{\text{op}}$-spin terms. Such spectral pairing deviations quantify the DTC lifetime as $τ_* \sim (1/λ)^{L/n_{\text{op}}}$. We further show that the analytical framework applies to generic DTC models with dominant Ising interaction and a given number of qubits, offering a unified scheme to quantify physical observables for systems beyond numerically accessible sizes, with or without disorders.

arXiv:2512.20707•Physical review. B./Physical review. B•Sep 11, 2026•0 citations

Scarred discrete time crystal in a periodically driven dimerized spin chain

Davood Marripour, Saeed S. Jahromi, Jahanfar Abouie

We investigate the emergence of a scarred discrete time crystal (SDTC) phase in a periodically driven dimerized spin chain. While generic interacting Floquet systems are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), we demonstrate that this system hosts quantum many-body scars (QMBS) that induce a regime of weak ergodicity breaking. Through an analysis of Floquet level statistics, entanglement entropy, and eigenstate fidelity, we identify a manifold of low-entanglement states characterized by semi-Poisson statistics embedded within an otherwise thermal spectrum. These scarred states support robust subharmonic oscillations with period doubling, signaling the spontaneous breaking of discrete time-translation symmetry. We show that the SDTC response is robust against a variety of initial state configurations, demonstrating its stability beyond fine-tuned conditions. A finite-size scaling analysis reveals that the time-crystalline lifetime grows with system size within the range accessible to our exact-diagonalization calculations. However, drawing on the general phenomenology of approximate many-body scars, we expect that hybridization between Floquet scars and the thermal continuum will eventually curtail this growth, causing the lifetime to saturate at system sizes beyond our current numerical reach. This characterizes the SDTC as a long-lived metastable dynamical regime rather than a strictly stable thermodynamic phase, providing a comprehensive framework for understanding the interplay between periodic driving and constrained many-body dynamics in disorder-free systems.

cond-mat.str-elCross-listedarXiv:2608.16616•Physical review. B./Physical review. B•Aug 18, 2026•0 citations

Homogeneous Floquet time crystal from weak ergodicity breaking

Hadi Yarloo, Ali Emami Kopaei, A. Langari

Recent works on the observation of discrete time-crystalline signatures throw up major puzzles on the necessity of localization for stabilizing such out-of-equilibrium phases. Motivated by these studies, we delve into a clean interacting Floquet system whose quasi-spectrum conforms to the ergodic Wigner-Dyson distribution, yet with an unexpectedly robust, long-lived time-crystalline dynamics in the absence of disorder or fine-tuning. We relate such behavior to a measure zero set of nonthermal Floquet eigenstates with long-range spatial correlations, which coexist with otherwise thermal states at near-infinite temperature and develop a high overlap with a family of translationally invariant, symmetry-broken initial conditions. This resembles the notion of ``dynamical scars'' that remain robustly localized throughout a thermalizing Floquet spectrum with fractured structure. We dub such a long-lived discrete time crystal formed in partially nonergodic systems, ``scarred discrete time crystal'' which is distinct by nature from those stabilized by either many-body localization or prethermalization mechanism.

arXiv:2007.14982•Physical review. B./Physical review. B•Dec 28, 2020•18 citations

Discrete time crystals enabled by Floquet strong Hilbert space fragmentation

Ling-Zhi Tang, Xiao Li, Z. D. Wang +1 more

Discrete time crystals (DTCs) are non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a disorder-free, periodically kicked XXZ spin chain, which is stabilized by the Floquet strong Hilbert space fragmentation. We numerically show the period-doubling response of the conventional DTC order, and uncover a multiple-period response with beating dynamics due to the coherent interplay of multiple $π$-pairs in the Floquet spectrum of small-size systems. The lifetime of the DTC order exhibits independence of the driving frequency and a power-law dependence on the ZZ interaction strength. It also grows exponentially with the system size, as a hallmark of the strong fragmentation inherent to the Floquet model. We analytically reveal the approximate conservation of the magnetization and domain-wall number in the Floquet operator for the emergent strong fragmentation, which is consistent with numerical results of the dimensionality ratio of symmetry subspaces. The rigidity and phase regime of the DTC order are identified through finite-size scaling of the Floquet-spectrum-averaged mutual information, as well as via dynamical probes. Our work establishes the Floquet Hilbert space fragmentation as a disorder-free mechanism for sustaining nontrivial temporal orders in out-of-equilibrium quantum many-body systems.

quant-pharXiv:2512.14182•Physical review. B./Physical review. B•Dec 17, 2025•3 citations

Discrete time crystal order in spin chains enabled by Floquet flat bands

Mahbub Rahaman, Anindita Roy

We propose a novel protocol to realize discrete time-crystal (DTC) order in clean, periodically driven spin-$1/2$ chains. In each drive cycle, a global spin flip is followed by a two-tone flat-band segment. This flat-band segment engineers a fully degenerate Floquet quasienergy spectrum, suppresses thermalization, and stabilizes a robust period-doubled subharmonic response. Using exact time evolution, we identify a pronounced subharmonic peak at half the drive frequency in the Fourier spectrum of the order parameter, thereby providing clear evidence for the emergence of stable DTC. The resulting phase is insensitive to system size, interaction strength, and interaction range; however, it remains sensitive to spin-rotation errors ($\varepsilon_r$), which can destabilize the subharmonic response. Compared with disorder-induced many-body localized (MBL) and disorder-free dynamically many-body localized (DMBL) DTCs, we find that the exact flat-band protocol offers a broader tunability of drive parameters, whereas MBL and DMBL based DTCs are more resistant to $\varepsilon_r$. In particular, the $\varepsilon_r$ sensitivity can be suppressed by incorporating additional spin-spin interactions that have modest deviations from the ideal flat-band protocol. This manifests itself in a robust DTC response over a finite window of spin-coupling strengths and drive frequencies. Our results establish flat-band driving as a versatile and experimentally relevant route to DTC order in disorder-free spin systems and motivate further exploration of nonequilibrium phases.

arXiv:2603.14307•Physical review. B./Physical review. B•Jul 1, 2026•0 citations
We reconstruct the spectral pairing theories to enable analytical descriptions of eigenstate spatiotemporal orders in translation-invariant system without prethermal conditions. It is shown that the strong Ising interactions and drivings alone stabilize a class of ``cat scar'' eigenstates with tunable patterns, which lead to local discrete time-crystal (DTC) dynamics. They exhibit Fock space localization and long-range correlations robust against generic perturbations in a disorder-free scenario. In particular, we introduce a symmetry indicator method to enumerate cat scars, with which a set of unexpected inhomogeneous scar patterns are identified in addition to the ferromagnetic scars found before. These scars enforce DTC dynamics with rigid inhomogeneous patterns, offering a viable way to verify underlying eigenstate properties experimentally. Further, we prove rigorously that the strong Ising interactions enforces a selection rule for perturbations of different orders, which imposes an exponential suppression of spin fluctuations for Floquet eigenstates. Based on this property, three analytical scaling relations are proved to characterize the amplitudes, Fock space localization, and lifetime for DTC dynamics associated with cat scars. We further provide two practical methods to check whether certain DTC phenomena are dominated by single-spin dynamics or due to genuine interaction effects.
We analytically identify a new class of quantum scars protected by spatiotemporal translation symmetries, dubbed Floquet-Bloch scars. They are distinguished from previous (quasi-)static scars by a rigid spectral pairing only possible in Floquet systems, where strong interaction and drivings equalize the quasienergy corrections to all scars and maintain their spectral spacings against generic bilinear perturbations. Scars then enforce the spatial localization and rigid discrete time crystal (DTC) oscillations as verified numerically in a trimerized kagome lattice model relevant to recent cold atom experiments. Our analytical solutions offer a potential scheme to understand the mechanisms for more generic translation-invariant DTCs.
Discrete time crystals (DTCs) have emerged as a novel non-equilibrium phenomenon. Nevertheless, analytical quantification for disordered DTCs remains challenging, leaving uncertainties about their behaviors in large scale systems amid current debates on the stability of (Floquet-)many-body localization. In this work, we introduce an analytical framework to calculate the values of key observables in a strongly disordered DTC without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement with numerical simulations for inverse participation ratios for eigenstate localization in Fock space, Edwards-Anderson parameters for spin-glass orders, mutual information for long-range entanglement, and the steady-state amplitudes of autocorrelators for period-doubled oscillations. Meanwhile, we demonstrate that eigenstate resonances render the scaling for the deviation of physical observables from their unperturbed values as O(λ)O(λ)O(λ), in contrast to non-resonant situations with suppressed deviation O(λ2)O(λ^2)O(λ2). Our newly developed scheme adopts resolvent perturbation formalism, which can directly prescribe arbitrarily higher-order corrections without iterations. With such advantages, we analytically prove that quasienergy corrections for pairwise cat eigenstates are identical up to order O(λ(L/nop)−1)O(λ^{(L/n_{\text{op}})-1})O(λ(L/nop​)−1), where perturbations of strength λλλ involve at most nopn_{\text{op}}nop​-spin terms. Such spectral pairing deviations quantify the DTC lifetime as τ∗∼(1/λ)L/nopτ_* \sim (1/λ)^{L/n_{\text{op}}}τ∗​∼(1/λ)L/nop​. We further show that the analytical framework applies to generic DTC models with dominant Ising interaction and a given number of qubits, offering a unified scheme to quantify physical observables for systems beyond numerically accessible sizes, with or without disorders.
We investigate the emergence of a scarred discrete time crystal (SDTC) phase in a periodically driven dimerized spin chain. While generic interacting Floquet systems are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), we demonstrate that this system hosts quantum many-body scars (QMBS) that induce a regime of weak ergodicity breaking. Through an analysis of Floquet level statistics, entanglement entropy, and eigenstate fidelity, we identify a manifold of low-entanglement states characterized by semi-Poisson statistics embedded within an otherwise thermal spectrum. These scarred states support robust subharmonic oscillations with period doubling, signaling the spontaneous breaking of discrete time-translation symmetry. We show that the SDTC response is robust against a variety of initial state configurations, demonstrating its stability beyond fine-tuned conditions. A finite-size scaling analysis reveals that the time-crystalline lifetime grows with system size within the range accessible to our exact-diagonalization calculations. However, drawing on the general phenomenology of approximate many-body scars, we expect that hybridization between Floquet scars and the thermal continuum will eventually curtail this growth, causing the lifetime to saturate at system sizes beyond our current numerical reach. This characterizes the SDTC as a long-lived metastable dynamical regime rather than a strictly stable thermodynamic phase, providing a comprehensive framework for understanding the interplay between periodic driving and constrained many-body dynamics in disorder-free systems.
Recent works on the observation of discrete time-crystalline signatures throw up major puzzles on the necessity of localization for stabilizing such out-of-equilibrium phases. Motivated by these studies, we delve into a clean interacting Floquet system whose quasi-spectrum conforms to the ergodic Wigner-Dyson distribution, yet with an unexpectedly robust, long-lived time-crystalline dynamics in the absence of disorder or fine-tuning. We relate such behavior to a measure zero set of nonthermal Floquet eigenstates with long-range spatial correlations, which coexist with otherwise thermal states at near-infinite temperature and develop a high overlap with a family of translationally invariant, symmetry-broken initial conditions. This resembles the notion of ``dynamical scars'' that remain robustly localized throughout a thermalizing Floquet spectrum with fractured structure. We dub such a long-lived discrete time crystal formed in partially nonergodic systems, ``scarred discrete time crystal'' which is distinct by nature from those stabilized by either many-body localization or prethermalization mechanism.
Discrete time crystals (DTCs) are non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a disorder-free, periodically kicked XXZ spin chain, which is stabilized by the Floquet strong Hilbert space fragmentation. We numerically show the period-doubling response of the conventional DTC order, and uncover a multiple-period response with beating dynamics due to the coherent interplay of multiple πππ-pairs in the Floquet spectrum of small-size systems. The lifetime of the DTC order exhibits independence of the driving frequency and a power-law dependence on the ZZ interaction strength. It also grows exponentially with the system size, as a hallmark of the strong fragmentation inherent to the Floquet model. We analytically reveal the approximate conservation of the magnetization and domain-wall number in the Floquet operator for the emergent strong fragmentation, which is consistent with numerical results of the dimensionality ratio of symmetry subspaces. The rigidity and phase regime of the DTC order are identified through finite-size scaling of the Floquet-spectrum-averaged mutual information, as well as via dynamical probes. Our work establishes the Floquet Hilbert space fragmentation as a disorder-free mechanism for sustaining nontrivial temporal orders in out-of-equilibrium quantum many-body systems.
We propose a novel protocol to realize discrete time-crystal (DTC) order in clean, periodically driven spin-1/21/21/2 chains. In each drive cycle, a global spin flip is followed by a two-tone flat-band segment. This flat-band segment engineers a fully degenerate Floquet quasienergy spectrum, suppresses thermalization, and stabilizes a robust period-doubled subharmonic response. Using exact time evolution, we identify a pronounced subharmonic peak at half the drive frequency in the Fourier spectrum of the order parameter, thereby providing clear evidence for the emergence of stable DTC. The resulting phase is insensitive to system size, interaction strength, and interaction range; however, it remains sensitive to spin-rotation errors (εr\varepsilon_rεr​), which can destabilize the subharmonic response. Compared with disorder-induced many-body localized (MBL) and disorder-free dynamically many-body localized (DMBL) DTCs, we find that the exact flat-band protocol offers a broader tunability of drive parameters, whereas MBL and DMBL based DTCs are more resistant to εr\varepsilon_rεr​. In particular, the εr\varepsilon_rεr​ sensitivity can be suppressed by incorporating additional spin-spin interactions that have modest deviations from the ideal flat-band protocol. This manifests itself in a robust DTC response over a finite window of spin-coupling strengths and drive frequencies. Our results establish flat-band driving as a versatile and experimentally relevant route to DTC order in disorder-free spin systems and motivate further exploration of nonequilibrium phases.