Breakdown of bosonic Thouless pump due to interaction in a quasiperiodic lattice

TL;DR

The paper investigates how on-site interactions affect the quantized Thouless pump in a bosonic quasiperiodic Aubry–André model. Using TEBD on strongly localized initial states, it shows that pumping quantization breaks down at weak interactions and that sharp changes arise from the closure of specific doublon channels, with quantization revived in the hardcore limit. It also reveals an asymmetric doublon stability depending on the band, where doublons in the lowest band remain robust under pumping while those in higher bands dissociate, transferring weight to lower bands and producing an energy decay unlike usual Floquet heating. These results highlight rich interaction-driven topology in driven quasiperiodic systems and point to future explorations across parameters and potential quantum-information applications.

Abstract

We investigate the effect of inter-particle interaction on the quantized Thouless pump in the bosonic quasiperiodic Aubry-Andr{é} model and find that the quantization of the pumped charge breaks down already for weak interactions. Furthermore, the pumped charge undergoes sharp changes as a function of interaction strength that we can attribute to the closing of specific doublon channels. As expected, the quantization revives in the hard-core limit at very large interaction strengths where the bosons are subject to a hardcore constraint. Interestingly, the stability of isolated doublons under the pump depends on the band they are in. For repulsive interactions and a suitably fixed pump period, doublons in the lowest band are pumped stably while doublons in higher bands dissociate during the pump with one particle decaying into a lower band. This asymmetry leads to the decay of the total energy over time, in stark contrast to the typical Floquet heating expected for a driven many-body system.

Figures (6)

• Figure 1: (a) Potential energy landscape (in arbitrary units with $\beta = \sqrt{2}/2$) of a one-dimensional Aubry-André model defined in Eq. \ref{['eq:hamiltonian']}. The parabolae show the potential minima of the lattice potential at different sites ($j$). The circles represent the sites and the quasiperiodic onsite energy ($\Delta_j$), and the blue shaded circles depict singly-occupied sites in the initial state. The two sites highlighted in red illustrate a resonance. As depicted in the inset, the variation of $\gamma$ during the pump gives rise to a Landau-Zener transition that pumps the particle from left to right and vice versa. The dotted line marks the position of the center of the first-order gaps in the single-particle spectrum. (b) Illustration of the hierarchical structure of gaps in the single-particle spectrum. The first-order gaps define the three bands (left) with different Chern numbers ($C$) and the higher-order gaps successively divide the bands into a fractal of sub-bands (second-order gaps shown on right).
• Figure 2: Time evolution of the particle ($n_i$) and doublon density ($d_i$) during the pump for $N=7$, $\Delta = 15J$, and for different values of $U$ shown in the upper and lower panels, respectively. For $U=0$, the initial cloud bifurcates into two branches with time, corresponding to the $C=-2$ and $C=1$ bands. For $U=2J$, $10J$, and $36J$, the time evolution of the density changes drastically compared to $U=0$. At very large $U=50J$, the time evolution of the density appears to be similar to the case of $U=0$. The time evolution of the doublon density is distinctly different in all cases (see the main text). System size is $L=40$ and results are averaged over $40$ realizations (i.e., 40 different values for $\gamma(0)$).
• Figure 3: Pumped charge in the time window from $t_1=2T$ to $t_2 = 3T$, normalized by the non-interacting case, as a function of interaction strength for $\Delta = 15J$ for (a) the right and (b) the left half of the system. The simulations employ a system size of $L=40$ sites, results are averaged over $40$ initial values of $\gamma(0)$, and are shown for three different particle numbers $N=5$, $N=6$, and $N=7$. The right insets show a magnified view of the weak-interaction regime, and the left inset in (b) shows how the ratio of $\bar{Q}_R/\bar{Q}_L$ changes as a function of interaction strength. The vertical dotted lines denote the values of $U$ where the system undergoes a sharp change in its behavior due to the resonances discussed in the text.
• Figure 4: The figure is divided into two parts, (a)-(e) and (f)-(j), corresponding to the dotted lines at $U_1\sim29J$ and $U_2\sim38J$ in Fig. \ref{['fig:QLR']}. In both cases we examine values of $U$ on both sides of the lines shown in Fig. \ref{['fig:QLR']} to highlight the contrast in the dynamics between a doublon channel being open or closed. (a) Solid lines denote the energy of a doublon on site $j$ and dotted lines correspond to pairs of singlons on sites $j$ and $j+2$. The initial phase of the quasiperiodic potential is $\gamma(0) = 0.4\pi$ and $U=28J<U_1$. (b) and (c) depict the evolution of particle ($n_j$) and doublon density ($d_j$) starting from a pair of particles on sites $j=0$ and $j=2$, corresponding to the orange dotted line in (a). The shaded area in (a) and red boxes in (b) and (c) indicate the time window where the energy of the initially occupied channel crosses with the doublon on site $j=0$. (f)-(j) Analogous plots around $U\sim 38J=U_2$ and $\gamma(0) = 0.6\pi$ with two particles initially on sites $j=-1$ and $j=1$. For $U=36J<U_2$, long-lived doublons form in the left half of the system, but this is strongly suppressed for $U=40J>U_2$.
• Figure 5: Illustration of the asymmetry in the stability of the doublon pump depending on its initial energy. The time evolution of the density is plotted for different values of $U$: $U=0$, $U=4J$, and $U=8J$. Here, two particles are initially placed at the central site for three initial values of $\gamma (0) = 1.2\pi$ (a-c), $0.8\pi$ (e-g), and $0.4\pi$ (i-k) that correspond to the energies belonging to lower ($C=1$) middle ($C=-2$), and upper ($C=1$) bands, respectively, for $U=0$. We see that, in the presence of interactions, the pumping of doublons in the lowest band remains stable, whereas it is unstable for the middle and upper band. To explain the presence or absence of stability in each case, we plot the energy channels formed by local doublon (solid lines) and singlon (dotted lines) states in (d), (h), and (l) for the parameters considered in (c), (g) and (k) respectively. The arrows represent the path followed by the initial state during the evolution. In the first case (lower band), the doublon successfully adiabatically moves from one site to the next site via a singlon state. In the other two cases (middle and upper band), the dynamics becomes non-adiabatic and the doublon fails to move to the other site.