Transport in a System with a Tower of Quantum Many-Body Scars

TL;DR

The paper investigates unconventional transport in a non-integrable spin-1 chain that hosts a tower of quantum many-body scars (QMBSs) generated by the ladder operator $J^5$, with scar energies equally spaced by $\omega=2h$. By analyzing the autocorrelation of a local ladder operator, the authors uncover a space-time pattern at momentum $k=\pi$ and frequency $\Omega=\omega$, and provide evidence for superdiffusive transport with $z\approx 3/2$, driven by the neighboring spectrum rather than the scars themselves. They prove that, in the thermodynamic limit, the autocorrelator is governed by states orthogonal to the scar subspace, establishing the irrelevance of scars for the long-time dynamics and motivating an extended ETH-like framework for scar-associated off-diagonal matrix elements. The work highlights a mechanism by which QMBSs interact with nearby energy levels to produce unconventional transport, with potential implications for experiments in Rydberg-atom and kinetically constrained systems, and suggests directions to generalize these insights to other scar-bearing models and universality classes. $z\approx 3/2$ and $\omega=2h$ appear as central quantitative signatures throughout the analysis.

Abstract

We report the observation of unconventional transport phenomena in a spin-1 model that supports a tower of quantum many-body scars, and we discuss their properties uncovering their peculiar nature. In quantum many-body systems, the late-time dynamics of local observables are typically governed by conserved operators with local densities, such as energy and magnetization. In the model under investigation, however, there is an additional dynamical symmetry restricted to the subspace of the Hilbert space spanned by the quantum many-body scars. The latter significantly slows the decay of autocorrelation functions of certain coherent states of quantum many-body scars and is responsible for the unconventional form of transport that we detect numerically. We show that excited states with energy close to that of the quantum many-body scars play a crucial role in sustaining the transport. Finally, we propose a generalized eigenstate thermalization hypothesis to describe specific properties of states with energy close to the scars.

Figures (6)

• Figure 1: Real part of the autocorrelator $\langle \mathcal{O}^\dagger (x,t) \mathcal{O}(0,0) \rangle_c$ for $\mathcal{O}=(S^{+}_{L/2})^2$. As time increases, a profile expands from the middle of the chain. Distinct even/odd effects and oscillations with period $2\pi/\omega \simeq 6.28$ are manifest, with $\omega = 2h$. The gradient is chosen to contrast the values between $-0.15$ (blue) and $0.15$ (purple). The parameters are $J =1, D=0.1, J_3 = 0.5, h=0.5, \zeta = -i$ and the size is $L=60$.
• Figure 2: Top panel: Rescaled profile of $\text{Re}[\langle \mathcal{O}^\dagger(x,t)\,\mathcal{O}(0,0)\rangle_c (-1)^x e^{i\omega t}]$ using the scaling ansatz in Eq. \ref{['eq:autocorr_osc']} with $z=3/2$. We plot different values of $t$, starting from $t=2$ (purple) until $t=8$ (yellow) with time step $\Delta t = 0.25$. Bottom panel: We show the time-dependence of $\eta(t)$ defined in the text; the plotted scalings $\propto t^{-1}$, $\propto t^{-1/2}$ and $\propto t^{-2/3}$ show the compatibility of the data with the latter.
• Figure 3: Rescaled profile of $\text{Re}[\langle \mathcal{O}^\dagger(x,t)\,\mathcal{O}(0,0)\rangle_c (-1)^x e^{i\omega t}]$ using the scaling ansatz in Eq. \ref{['eq:autocorr_osc']} with $z=2$ (top panel) and with $z=1$ (bottom panel), by considering the (rescaled) spatial profiles at different values of $t$, starting from $t=2$ (purple) until $t=8$ (yellow) with time step $\Delta t = 0.25$. The plotted data are those presented in Fig. \ref{['fig:collapse']}.
• Figure 4: We show the absolute value of the autocorrelator of $\mathcal{O}=(S^{+}_{L/2})^2$ in the infinite temperature state, for $t\in[0,5]$ in a chain of length $L=60$. A quick decay, starting from the value $4/3\simeq 1.33$ at $t=0$, is observed in time and the spatial support does not grow, differently from what we observed for the coherent state.
• Figure 5: Off-diagonal matrix element $|\langle E_i | (S^{+}_j)^2 | N \rangle|^2$, with $j = L/2$, as a function of the energy difference $E_i - N \omega$. We choose $N=L/2$, so that the scars $\ket{N},\ket{N+1}$ have magnetization $0,2$ respectively. The red square point represents $|\langle N+1 | (S^{+}_{L/2})^2 | N \rangle|^2$, which is far larger compared to the other exponentially small overlaps. The points are calculated via exact diagonalization for $L=10$. The color scheme illustrates the density of points.