Anyons obey fractional statistics that lie between bosonic and fermionic statistics, giving rise to a broad range of intriguing phenomena. However, how anyonic statistics govern quantum-state complexity is still largely unexplored. In this work, we investigate the interplay between the statistical phase and on-site interactions in the anyon-Hubbard model, identifying exact quantum many-body scar eigenstates and novel quench dynamics. The Krylov complexity exhibits perfect periodic revivals independent of the statistical phase in the scarred dynamics, whereas after a quench it depends on both the statistical phase and the interaction strength. In the strong-interaction regime, we find approximate scarred dynamics, while in the weak-interaction regime the state spreads over Krylov space and the complexity ultimately saturates. Moreover, for the bosonic initial state, the complexity of fermions exhibits the lowest saturation value, and vice versa. For fractional statistics, the saturation plateau is minimized when the post-quench statistical phase is close to that of the initial state. Our results demonstrate the central role of the statistical phase in governing many-body dynamics and provide new insights into Krylov complexity and quantum many-body scars.
Anyons obey fractional statistics that lie between bosonic and fermionic statistics, giving rise to a broad range of intriguing phenomena. However, how anyonic statistics govern quantum-state complexity is still largely unexplored. In this work, we investigate the interplay between the statistical phase and on-site interactions in the anyon-Hubbard model, identifying exact quantum many-body scar eigenstates and novel quench dynamics. The Krylov complexity exhibits perfect periodic revivals independent of the statistical phase in the scarred dynamics, whereas after a quench it depends on both the statistical phase and the interaction strength. In the strong-interaction regime, we find approximate scarred dynamics, while in the weak-interaction regime the state spreads over Krylov space and the complexity ultimately saturates. Moreover, for the bosonic initial state, the complexity of fermions exhibits the lowest saturation value, and vice versa. For fractional statistics, the saturation plateau is minimized when the post-quench statistical phase is close to that of the initial state. Our results demonstrate the central role of the statistical phase in governing many-body dynamics and provide new insights into Krylov complexity and quantum many-body scars.
Weak ergodicity breaking, particularly through quantum many-body scars (QMBS), has become a significant focus in many-body physics. Krylov state complexity quantifies the spread of quantum states within the Krylov basis and serves as a powerful diagnostic for analyzing nonergodic dynamics. In this work, we study spin-one XXZ magnets and reveal nonergodic behavior tied to QMBS. For the XY model, the nematic N\'eel state exhibits periodic revivals in Krylov complexity. In the generic XXZ model, we identify spin helix states as weakly ergodicity-breaking states, characterized by low entanglement and nonthermal dynamics. Across different scenarios, the Lanczos coefficients for scarred states display an elliptical pattern, reflecting a hidden SU(2) algebra that enables analytical results for Krylov complexity and fidelity. These findings, which exemplify the rare capability to characterize QMBS analytically, are feasible with current experimental techniques and offer deep insights into the nonergodic dynamics of interacting quantum systems.
Anyons, namely particles obeying fractional quantum statistics that interpolate between bosons and fermions, possess a lot of new and exotic physical properties related to the particle exchange statistics. In this work, we explore the few-body quantum dynamics and quantum correlations of indistinguishable anyons with on-site interactions in onedimensional lattices within the scheme of three-body continuous-time quantum walks. By employing a time-evolving block decimation (TEBD) algorithm, we numerically calculate the dynamical evolution process of the local density distribution of anyons among the whole lattice. Numerical simulations shown in the main text mainly focus on a threebody initial state as ψ|(t=0)＞=â†-1â†0â†1|0＞, in which three particles are located on neighbouring sites at lattice centre. This choice of initial state features that the three particles influence one another most strongly, while we have also implemented numerical simulations on other choices of three-body initial states as are discussed in appendix. It is shown that the local density distribution of anyons is dramatically altered by fractional particle statistics with new dynamical structure showing up during the time evolution. For free anyons, an inner cone emerges as the statistical parameter increases, while the outer cone remains robust all along. When the on-site interaction joins in, the structure of the inner cone is further modified with new features. Specifically, for interaction of finite strength, an exotic dynamical asymmetry in real space, is clearly demonstrated during the time evolution of the local density distribution for particles within the fractional statistics regime. However, for boson limit and pseudofermion limit, the time evolution of the local density distribution keeps symmetric as the three-body initial state. And remarkably, the dynamical asymmetry is interactiondependent manifested as the local density distribution of anyons favors opposite side of the lattice for repulsive and attractive interaction, respectively. Moreover, when the on-site interaction is further increased to hard-core limit, the dynamical asymmetry will then be largely suppressed. We also calculate the density-density correlations for anyons before they reach the lattice boundary to reveal the interesting effect of fractional statistics on quantum correlations. It is shown that the inner cone corresponds to co-walking of anyons, while the outer cone is related to individual walking and is immune to the variation of statistical parameter. Furthermore, the exotic real-space asymmetry originated from the interplay of fractional statistics and finite interaction is also shown up in the density-density correlations.
We investigate the anatomy and complexity of quantum states in Krylov space, in the ergodic and many-body localised (MBL) phases of a disordered, interacting spin chain. The Krylov basis generated by the Hamiltonian from an initial state provides a representation in which the spread of the time-evolving state constitutes a basis-optimised measure of complexity. We show that the long-time Krylov spread complexity sharply distinguishes the two phases. In the ergodic regime, the infinite-time complexity scales linearly with the Fock-space dimension, indicating that the state spreads over a finite fraction of the Krylov chain. By contrast, it grows sublinearly in the MBL regime, implying that the long-time state occupies only a vanishing fraction of the chain. Further, the profile of the infinite-time state along the Krylov chain exhibits a stretched-exponential decay in the MBL regime. This behaviour reflects a broad distribution of decay lengthscales, associated with different eigenstates contributing to the long-time state. Consistently, a large-deviation analysis of the statistics of eigenstate spread complexities shows that while the ergodic regime receives contributions from almost all eigenstates, the complexity in the MBL regime is dominated by a vanishing fraction of eigenstates, which have anomalously large complexity relative to the typical ones.
We investigate Krylov state complexity in a tilted extended Bose-Hubbard chain in which both the on-site interaction U and nearest-neighbor interaction V are present. The tilted extended Bose-Hubbard model can be realized with Rydberg-dressed interactions in optical lattices. Using exact diagonalization and Lanczos recursion from three physically motivated Fock states, we compute the time-dependent complexity, its long-time saturation value, and the fluctuations of the Lanczos coefficients for an open chain at unit filling. Crucially, we identify a pronounced quasi-chaotic diagonal regime near U≃V in which the Krylov complexity saturation exhibits a sharp ridge while the spectral level-spacing statistics remain partially chaotic. This dissociation arises from the competition between the on-site and nearest-neighbor interaction, which generates a dense manifold of near-resonant many-body configurations that is efficiently coupled by the state-dependent dynamics but retains residual spectral structure. Our results show that Krylov state complexity provides complementary, state-sensitive information about many-body chaos that is not captured by the spectral diagnostics alone, establishing Krylov complexity as a useful diagnostic for studying thermalization and information scrambling in experimentally accessible quantum simulators.
We study the quantum dynamics of two interacting anyons in the Anyon-Hubbard model on a four-site plaquette, a system that is exactly mappable to a Bose-Hubbard model. We reveal that static Aharonov-Bohm (AB) caging, induced by only specific statistical phases, emerges in the strongly interacting limit but breaks down under weak interparticle interactions. To address this, we demonstrate that statistical-factor-induced AB caging can be dynamically restored via Floquet engineering. This dynamical mechanism, governed by the synthetic Floquet flux and the anyonic statistical phase, extends the caging effect into the weakly interacting regime across the full spectrum of statistical phases. Furthermore, we show that the external drive enables the selective caging of anyons, providing an efficient approach for manipulating anyons and identifying statistical phases.
Thermalization in closed quantum systems and its breakdown are central to understanding the emergence of statistical behavior in isolated many-body systems. Kinetic constraints can hinder thermalization by restricting the allowed dynamics and giving rise to non-ergodic behavior. While various aspects of ergodicity breaking in kinetically constrained models have been extensively studied in Hermitian systems, their behavior in non-Hermitian kinetically constrained models remains less explored. In particular, the inequivalence of left and right eigenstate ensembles in non-Hermitian systems raises the question of whether they exhibit qualitatively different dynamical and eigenstate properties. In this work, we study non-Hermitian generalizations of the paradigmatic PXP and PPXPP models, focusing on their Krylov complexity, eigenstate structure, and dynamics. By exploiting the Arnoldi's algorithm, we find distinct behavior of Krylov complexity in the left and right eigenstate ensembles as non-Hermiticity is increased: in the right ensemble, it exhibits persistent oscillations with an increasing period, while in the left ensemble, it gradually saturates. The characteristic arch-shaped profile of the Arnoldi coefficients is also modified differently in the two ensembles, with a Hermitian-like arch re-emerging in the left ensemble at large non Hermiticity. Additionally, in the non-Hermitian PXP model, the right ensemble retains the characteristic scar structure, while the left ensemble develops additional non-scar eigenstates with anomalously low entanglement and large overlap with the vacuum state. These findings reveal that non-Hermiticity can affect Krylov dynamics and eigenstate structure differently in the left and right ensembles, demonstrating the need to treat them separately when characterizing non-Hermitian kinetically constrained systems.