Quantum information scrambling in strongly disordered Rydberg spin systems

TL;DR

The paper addresses how quantum information scrambles in strongly disordered spin systems with power-law interactions by analyzing out-of-time-order correlators (OTOC). It combines numerical simulations of a disordered XXZ chain with both nearest-neighbor and power-law couplings and a Floquet-based experimental protocol to measure OTOCs in Rydberg tweezer arrays, demonstrating how long-range interactions modify scrambling under strong disorder. The key finding is that power-law interactions yield algebraic light cones with t_theta proportional to r^beta, where beta is about 1.48 in the tail for alpha = 3 and 6, in contrast to logarithmic light cones for NN, and an analytical Ising bound explains a soft cutoff in growth; the work also discusses how disorder distributions influence slow-growth realizations. The authors propose practical state preparation and time-reversal strategies to estimate infinite-temperature OTOCs and show that random bitstring state ensembles can be efficient for large systems. Overall, the results reveal a nontrivial interplay between disorder and long-range interactions in information scrambling and provide a feasible route to experimentally probe scrambling in programmable quantum simulators.

Abstract

Despite the fact that power-law interactions occur in a plethora of physical systems, their many-body dynamics is far less understood than that of nearest-neighbor interacting systems. Here, we study information scrambling in strongly disordered spin systems with power-law interactions via out-of-time-order correlators (OTOCs). Numerically, we find pronounced differences in the dynamical spreading of OTOCs between nearest-neighbor and power-law interacting systems. This deviation persists even for short-range interactions, opposing the common view that these interactions produce dynamics equivalent to the nearest-neighbor case. In a detailed experimental proposal, tailored but not limited to Rydberg tweezer setups, we present a protocol to extract OTOCs in XXZ Heisenberg spin systems with tunable anisotropy and programmable disorder based on currently available techniques.

Figures (5)

• Figure 1: Operator growth in the strongly disordered regime.a) Out-of-time-order commutators $C_x(r,t)=\norm{[\hat{\sigma}^x_3(t),\hat{\sigma}_j^x]}_F^2$ for the Heisenberg XXZ model with nearest-neighbor or dipolar interactions at strong disorder $h=14$. Shown is the disorder average over 5000 individual shots at a system size of $N=13$. The indicated marks correspond to thresholds $C_x(r,t_\theta)=\theta$ with $\theta \in \{0.25,\,0.5,\,1\}$ and dashed lines are fits $t_\theta \propto e^{\beta r}$, and $t_\theta \propto r^\beta$. b) Vertical cuts through the light cones in (a) showing the time evolution of $C_x(r,t)$ at different distances $r$.
• Figure 2: Ensemble of Disorder Realizations Distribution of out-of-time-order commutators $C_x(r,t)$ over 5000 individual disorder realizations ($h=14$) for nearest-neighbor and dipolar interactions, exemplified for $r=3$ ($N=13$). The red curves correspond to the disorder average and the probability of $C_x(r=3,t)$ to take a given value is indicated by the estimated probability density functions (PDF, color background). The dashed white curve in the lower panel shows the (disorder-independent) analytical solution $C^I_x(r=3,t)$ for power-law Ising interactions.
• Figure 3: Operator Growth for vdW interactionsa) Out-of-time-order commutators $C_x(r,t)=\norm{[\hat{\sigma}^x_3(t),\hat{\sigma}_j^x]}_F^2$ for the Heisenberg XXZ model with vdW interactions at strong disorder $h=21$. Shown is the disorder average over 5000 individual shots at a system size of $N=13$. The indicated marks correspond to thresholds $C_x(r,t_\theta)=\theta$ with $\theta \in \{0.25,\,0.5,\,0.75\}$ and dashed lines are fits $t_\theta \propto e^{\beta r}$. b) Time evolutions of $C_x(r,t)$ at different distances $r$ for nearest-neighbor (dashed) and vdW (solid) interactions at $h=14$ and $h=21$. The distribution of $C_x(r=3,t)$ sampled across 5000 disorder realizations at $Jt\sim 100$ (vertical dashed line) is illustrated in c). The vertical line indicates the value of $C^I_x$ and the fractions of realizations with slower growth are quantified next to the histogram for both types of interactions.
• Figure 4: Measurement Sequencea) Sequence of steps for measuring OTOCs. The time-reversal is achieved by transferring the states between two spin-1/2 encodings in the Rydberg manifold, effectively changing $C_3$ to $-kC_3$. Periodic driving can be applied during forward and backward evolution to realize an effective Floquet Hamiltonian. b) The WAHUHA sequence used for introducing $\hat{\sigma}_i^z\hat{\sigma}_j^z$-interactions to obtain an XXZ model. c) Our proposed and modified sequence designed to cancel out fields in $x$- and $y$-directions and to implement the XXZ model with random on-site disorder. d) Performance of our proposed sequence. We compute the out-of-time-order commutators $C_x(r,t) = \bra{\psi}[\hat{\sigma}_3^x(t),\hat{\sigma}_j^x]\ket{\psi}$ exactly (black dashed line) and with Floquet forward and backward propagation for three disorder strengths and a cycle time of $t_c=0.1J^{-1}$. For comparison, a single, but for both sequences same, disorder realization is used. The initial state is chosen as a Néel state along $x$, the anisotropy is $\Delta=0.5$ and system size is $N=13$.
• Figure 5: Initial State Sampling Standard error of the mean (SEM) of $\overline{C}_z$ as a function of number of sample states $n_s$, where $\overline{C}_z$ represents the average of $C^\psi_z(r,t)$ over all distances and 20 timesteps from $Jt = 0.1$ to $Jt = 2$. It is shown for three ensembles of initial states and system sizes $N\in\{13,15,17,19,21\}$. The inset highlights the variation of $C_z(r=3,t)$ for distinct initial states $\Ket{\psi}$ and uses the same colors for the different ensembles as the main panel.