Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics

We study the nonequilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast to the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through nonequilibrium dynamics.

Figure 1

Density expansion dynamics for particles initially localized one per site in the central $N$ sites, with different statistical angles $\theta$ and interaction strengths $U$. In all plots, the particle number is $N=4$ and the lattice size is $L=30$. (a)–(b) Bosonic cases with zero and nonzero interactions, respectively. (c) Pseudofermionic case ($\theta =\pi$) with nonzero interactions. (d)–(h) Anyonic cases with various values for $\theta$ and $U$.

Figure 2

(a) Particle number difference $\mathrm{\Delta }N$ between the right and left halves versus anyon angle $\theta$ at time $t=4$, which is beyond the perturbative regime yet occurs before the quench hits the boundary. The interaction strength is $U=4$. (b) $\mathrm{\Delta }N$ versus interaction strength $U$ at time $t=4$, with $\theta =\pi /3$. The particle number is $N=4$, and the lattice size is $L=30$ for both plots, just as in Fig. 1.

Figure 3

OTOC growth $|F_{jk}(t)|$ for different statistical angles $\theta$ and interaction strengths $U$. Here, $L=7$, ${\beta }^{-1}=6$, $k=4$, and the local Hilbert space of each site is truncated to three states. Plotted is (a) a bosonic case ($\theta =0$) with nonzero interaction, as well as anyonic cases with (b) vanishing and (c), (d) nonvanishing interaction strengths. The red dots denote where the OTOCs fall to 75% of their initial values. The color maps are interpolated to noninteger $j$ to better illustrate the light cone behavior.

Figure 4

(a) OTOC growth characterizing quantum information spreading from the leftmost site, $k=1$, rightward. The OTOC starts to fall when information reaches the $j$th site, and the black arrows denote the OTOCs’ fall to 99% of their initial values. Parameters: $\theta =\pi /3$, $U=2$, $L=7$. (b) Same as (a) but shows information spreading from the rightmost site $k=7$ toward the left. Inset: linear fit to extract the butterfly velocities for left (blue) and right (red) directions, respectively. (c) Left ($V_b^l$) and right ($V_b^r$) butterfly velocities’ dependence on statistical angle $\theta$ when $U=2$. Inset: velocity ratio $r=V_b^l/V_b^r$ versus angle $\theta$. (d) Dependence of $V_b^l$ and $V_b^r$ on interaction strength $U$ when $\theta =\pi /2$. Inset: velocity ratio $r=V_b^l/V_b^r$ versus interaction strength $U$.