Quantum walks of interacting Mott-insulator defects with three-body interactions

Quantum walks of interacting particles may display nontrivial features due to the interplay between the statistical nature and the many-body interactions associated with them. We analyze the quantum walk of interacting defects on top of a uniform bosonic Mott insulator at unit filling in a one-dimensional graph. While the quantum walk of a single-particle defect shows trivial features, the case of two particles exhibits the interesting phenomenon of quantum walk reversal as a function of additional on-site three-body attractive interactions. In the absence of a three-body interaction a quantum walk of pairs of particles is obtained, and as the strength of the three-body interaction becomes more and more attractive, independent-particle behavior appears in the quantum walk. Interestingly, further increase in the three-body interaction leads to the reappearance of the quantum walk associated with a pair of particles. This quantum walk reversal phenomenon is studied using the real-space density evolution, Bloch oscillation, and two-particle correlation functions.

Figure 1

Top panel: The initial state, which is two particles on top of a bosonic Mott insulator in one dimension at unit filling, i.e., $a_0^{{†}^2}|{\mathrm{MI}}_1\rangle$. Here $J$ denotes the hopping strength. Bottom panel: Phenomenon of QW reversal shown as a function of the three-body attractive interaction.

Figure 2

(a) Time evolution of $\langle n_i\rangle$ of a single defect with $J=0.2$ and $U=10$ on an MI background of length $L=29$ sites. (b) Propagation of the entanglement entropy $S$ shows the linear spread of information.

Figure 3

The phenomenon of QW reversal of a pair of defects shown in terms of the density evolution on a homogeneous (a–g) and a tilted (h–n) lattice. In the case of the tilted lattice the period doubling in the Bloch oscillation clearly indicates the QW of a bound defect pair.

Figure 4

Normalized two-particle correlation functions ${\mathrm{\Gamma }}_{ij}$ plotted with respect to positions $i$ and $j$ after a time evolution of 11.25 in units of ($1/J$) for $t=0.2$, $U=10$, and different values of $W/U$—(a) $-0.5$, (b) $-0.8$, (c) $-0.9$, (d) $-1.0$, (e) $-1.1$, (f) $-1.2$, and (g) $-1.5$—on a homogeneous one-dimensional lattice of length $L=29$. The density distribution is shown at the top of each correlation plot.