Asymmetric and chiral dynamics of two-component anyons with synthetic gauge flux

TL;DR

The paper investigates non-equilibrium expansion in a 1D two-component anyon-Hubbard model with density-dependent hopping and synthetic gauge flux, revealing asymmetric transport and two dynamical symmetries. By mapping to an extended Bose-Hubbard ladder, it uses exact diagonalization and symmetry analysis to show how θ and φ control time-reversal and inversion properties, with spreading suppressed in the non-interacting limit and tunable chiral/antichiral dynamics emerging under interactions. The work provides a detailed symmetry-based framework and phase diagram for multi-component anyons, highlighting the interplay between exchange statistics, synthetic gauge fields, and interactions. These findings advance the understanding of dynamical phenomena in engineered anyonic systems and guide future experimental explorations.

Abstract

In this work, we investigate the non-equilibrium dynamics in a one-dimensional two-component anyon-Hubbard model, which can be mapped to an extended Bose-Hubbard ladder with density-dependent hopping phase and synthetic gauge flux. Through numerical simulations of two-particle dynamics and the symmetry analysis, we reveal the asymmetric transport with broken inversion symmetry and two dynamical symmetries in the expansion dynamics. The expansion of two-component anyons is dynamically symmetric under spatial inversion and component flip, when the sign of anyonic statistics phase or the signs of gauge flux and interaction are changed. In the non-interacting case, we show the dynamical suppression induced by both the statistics phase and gauge flux. In the interacting case, we demonstrate that both chiral and antichiral dynamics can be exhibited and tuned by the statistics phase and gauge flux. The dynamical phase regimes with respect to the chiral-antichiral dynamics are obtained. These findings highlight the rich dynamical phenomena arising from the interplay of anyonic exchange statistics, synthetic gauge fields, and interactions in multi-component anyons.

Figures (6)

• Figure 1: Schematic of the lattice of interacting two-component anyons under an artificial magnetic flux denoted by $\phi$. Here, $J$ denotes the hopping amplitude, $U$ is the Hubbard interaction strength, and $\Omega$ represents the coupling strength between two components. One-dimensional anyons with two components have an exchange phase $\theta$ that interpolates between 0 and $\pi$.
• Figure 2: (Color online) (a-d) $D^{(1)}_{\uparrow}$, $D^{(1)}_{\downarrow}$, $\Delta N$ and $\Delta D^{(2)}$ as a function of $\theta$ or $\phi$ at the time $t=2$ (in units of $\hbar/J$). The non-interacting and interacting cases with $U/J=0$ and are $U/J=4$ are shown in (a,b) and (c,d), respectively. We set $\phi=\pi/4$ in (a,c) and $\theta=\pi/4$ in (b,d). Time evolution of density distributions for (e) $U/J=0$ and (f) $U/J=4$ with fixed $\theta=\pi/4$ and $\phi=\pi/2$. Other parameters in (a-f) are $\Omega/J=1$ and $L=26$.
• Figure 3: (Color online) Time evolution of $D^{(1)}_{\uparrow}$ and $D^{(1)}_{\downarrow}$ for (a) $\theta=\pm\pi/4$ and (b) $\phi=\pm\pi/4$ and $U/J=\pm4$. $\Delta D^{(1)}$ in (c) the $\theta$-$\phi$ plane and (d) the $U$-$\phi$ plane at the time $t=4$ (in units of $\hbar/J$). Other parameters are $\Omega=1$ and $L=26$ in (a-e), $\phi=\pi/4$ and $U/J=4$ in (a), $\theta=\pi/4$ in (b), $U/J=4$ in (c), and $\theta=\pi/4$ in (d).
• Figure 4: (Color online) $\overline{D^{(2)}}(t)$ at the time $t=2$ (in units of $\hbar/J$) as a function of (a) $\theta$ with $\phi=0,\pi/4$, and (b) $\phi$ with $\theta=0,\pi/4$. Time evolution of density distributions for (c) $\theta=0$ and $\phi=0$; (d) $\theta=\pi/2$ and $\phi=0$; (e) $\theta=\pi/2$ and $\phi=\pi/2$; and (f) $\theta=\pi$ and $\phi=\pi/2$. Other parameters in (a-f) are $\Omega/J=1$, $U/J=0$, and $L=26$.
• Figure 5: (Color online) Time evolution of $D^{(1)}_{\uparrow}$ and $D^{(1)}_{\downarrow}$ for (a) $\theta=0$ and (b) $\theta=\pi/2$. Time evolution of density distributions for (c) $\theta=0$ and (d) $\theta=\pi/2$. Other parameters in (a-d) are $U/J=4$, $\Omega/J=1$, $\phi=\pi/6$, and $L=26$.