Anomalous dynamical scaling in interacting anyonic chains

Abstract

Particle statistics impose fundamental constraints on nonequilibrium quantum dynamics, yet it remains an open question whether fractional statistics can lead to emergent universal dynamical scaling beyond the conventional Bose-Fermi paradigm. Here we investigate the far-from-equilibrium many-body relaxation of anyons in a one-dimensional lattice and uncover an unconventional yet universal scaling behavior governed by fractional statistics. Based on large-scale numerical simulations and scaling analysis, we identify a distinct separation between particle transport and information spreading: density correlations spread superdiffusively, whereas entanglement entropy grows ballistically. The anomalous particle dynamics can be interpreted intuitively from the statistical-phase-induced quantum interference, which suppresses coherent holon-doublon propagation. In contrast, the entanglement growth turns out to be dominated by its configurational component, which propagates ballistically. Our results establish anyonic statistics as a distinct source of universal nonequilibrium dynamics beyond bosons and fermions, with direct relevance to current quantum simulation experiments.

Figures (11)

• Figure 1: Anomalous far-from-equilibrium dynamical scaling in a 1D interacting anyonic system. (a) Schematic of a 1D anyonic lattice with hopping $J$, mapped onto a BHM with density-dependent tunneling $Je^{i\theta n}$ and interactions $U$, where $n$ and $\theta$ denote the local density and statistical angle, respectively. A quantum quench from an out-of-equilibrium state triggers the spreading of spatial correlations and entanglement throughout the system. (b) Distinct scaling of the half-chain particle-number fluctuations $\Delta N$ and the von Neumann entanglement entropy $S$. Both quantities are shown as functions of statistical angle $\theta$ and time $t$: for $U\leq J$, $\Delta N$ crosses over from ballistic to superdiffusive as $\theta$ increases from $0$ to $\pi$, while $S$ remains ballistic.
• Figure 2: Dynamical scaling of the correlation distance and particle-number fluctuations. (a)(b) In the noninteracting regime ($U=0$), (a) time evolution of the correlation distance $l(t)$ for statistical angles $\theta\in[0,\pi]$, revealing a crossover from ballistic growth ($\beta=1$) to superdiffusive scaling ($\beta=2/3$) (see inset); (b) half-chain particle-number fluctuations $\Delta \widetilde{N}(t)$, exhibiting a scaling collapse with dynamical exponent $z=3/2$ (inset: unscaled data for $\theta=\pi$). (c) Time evolution of $l(t)$ in the strongly interacting regime ($U/J=100$) for $\theta\in[0,\pi]$, exhibiting an approximately ballistic scaling with $z\approx 1$. (d) Scaling exponent $\beta$ extracted from $l(t)$ over a broad range of interaction strengths $U/J=0.01$--$100$ at statistical angles $\theta=0$, $\pi/2$, and $\pi$, demonstrating a universal scaling regime for $U\leq J$. Numerical results of $l(t)$ are obtained for system size $L=100$ with bond dimensions up to $1500$.
• Figure 3: Dynamical scaling of entanglement entropy in the relaxation dynamics of the anyonic chain described by $\hat{H}$. (a) Rescaled von Neumann entropy $\widetilde{S}(t)$ as a function of time $t$ for $\theta=\pi/2$, with the inset showing the unrescaled data. The nearly ballistic scaling with $z\simeq1$ demonstrates a clear separation between entanglement propagation and particle transport [Fig. \ref{['figure-2']}(d)]. (b) Schematic illustration of the reduced density matrix $\rho_A$, where the total entanglement entropy $S$ is decomposed into the number entropy $S_N$, associated with particle-number fluctuations between sectors, and the configuration entropy $S_C$, arising from superpositions within each particle-number sector. (c) Number entropy $\widetilde{S}_N(t)$ and (d) configuration entropy $\widetilde{S}_C(t)$ for $\theta=\pi/2$. Throughout the evolution, the entanglement growth is dominated by $S_C$ (insets). Results are obtained for system sizes $L=10$--$14$ at interaction strength $U/J=0.2$, using bond dimensions up to 4000.
• Figure 4: Diagram of interference picture of holon-doublon pairs under anyonic statistics and experimental realization. (a) Schematic illustration of holon-doublon propagation starting from an initially adjacent holon-doublon pair ($d=1$) to separation $d=3$ via two distinct hopping paths. Paths along these trajectories acquire $\theta$-dependent phases, leading to destructive interference that suppresses the propagation of the pairs. (b) Density deviation dynamics $\delta n_j(t)$ governed by Eq. (\ref{['eq:Ham']}), after a central-site excitation for the bosonic (left, $\theta=0$), anyonic (middle, $\theta=\pi/2$), and pseudofermionic (right, $\theta=\pi$) cases. (c) Floquet protocol realized in Ref. kwan24: three-tone modulation $V = \sum V_i$ (solid) resonantly restores tunneling in a tilted lattice; $V_{1,2,3}$ (dashed, dotted, dot-dashed) selectively drive singly-to-empty, singly-to-singly, and doubly-to-empty transitions. The phase offset $\theta$ of $V_3$ implements the density-dependent Peierls phase. (d) Density deviation dynamics $\delta n_j(t)$ for the setup in (c). The agreement demonstrates the robust realization of anyonic dynamics in the many-body regime. Time $t$ is in units of $1/J$ in (b) and $1/J'$ in (d), with $J'$ the effective Floquet hopping rate SM. Results are obtained for a system of size $L=100$ in the weakly interacting regime ($U/J=0.2$).
• Figure S1: Dependence of the correlation transport distance $l(t)$ on numerical control parameters: (a,b) bond dimension, (c,d) system size $L$, (e,f) time step $dt$, and (g,h) local occupation cutoff $N_m$. The parameters used in the main text are a bond dimension of 1500 for $\theta=0$ and 2000 for $\theta=\pi$, with $L=100$, $dt=0.01$, and $N_m=5$.