Proposal for many-body quantum chaos detection with single-site measurements

TL;DR

This work addresses identifying many-body quantum chaos from limited experimental access by using single-site measurements. It demonstrates that long-time dynamics of the partial survival probability $S_P^{(L_s,L)}(t)$ and the spin autocorrelation function $C^z_{(L_s,L)}(t)$ reveal the correlation hole characteristic of random-matrix-like spectral correlations, even when only a single lattice site is observed in small disordered spin chains. The approach is studied in a disordered isotropic spin-1/2 Heisenberg chain with onsite disorder $h$ and nearest-neighbor coupling $J$, and the correlation hole dynamics scale with the Hilbert-space dimension as $t_{\mathrm{ramp}} \sim D^{2/3}$ and $t_H \sim D$, making full observation challenging but feasible for $L\sim 6$–$8$. The results show that spin autocorrelation is particularly robust to the measurement subset, allowing a single-site readout to reveal chaos, while partial survival probability benefits from measuring multiple central sites; random couplings further smooth the signals. Overall, the findings indicate that dynamical fingerprints of many-body quantum chaos can be detected with existing technology without full-spectrum access, enabling experimental tests of RMT-based chaos diagnostics and thermalization.

Abstract

We demonstrate that the long-time dynamics of an observable associated with a single lattice site is sufficient to determine whether a many-body quantum system exhibits level statistics characteristic of random matrix theory, a widely used diagnostic of quantum chaos. In particular, we focus on the partial survival probability and spin autocorrelation function at a single site, both evolved under a disordered spin-1/2 chain, which is a setup realizable in current experimental platforms. Given the precision and timescales currently achievable, our results indicate that the detection of many-body quantum chaos is feasible, but constrained to small system sizes.

Figures (6)

• Figure 1: Partial survival probability for a chain with (a)-(c) $L=6$ and (d)-(f) $L=12$. The horizontal dashed line indicates the saturation value of $S_P^{(L_s,L)}(t)$. The measurement is performed over a subsystem of size $L_s$, as indicated in the panels.
• Figure 2: Spin autocorrelation function for a chain with (a)-(c) $L=6$ and (d)-(f) $L=12$. The horizontal dashed line indicates the saturation value of $C^z_{(L_s,L)}(t)$. The measurement is performed and averaged over $L_s$, as indicated in the panels.
• Figure 3: Comparison between the evolution of the spin autocorrelation function on the central site, $\langle A^z_{L/2}(t) \rangle$, with the evolution of the survival probability $\langle S_P(t) \rangle$ and the two other terms in Eq. (\ref{['eq_Imb_SP']}): $\langle P_{L/2}^{n_0'}(t)\rangle$ and $\langle P_{L/2}^n(t)\rangle$.
• Figure 4: (a)-(d) Density of states and (e)-(h) level spacing distribution for (a),(e) $L=6$; (b),(f) $L=8$; (c),(g) $L=10$; and (d),(h) $L=12$. Averages are performed over disorder realizations. Red solid line indicates (a)-(d) Gaussian distribution and (e)-(h) Wigner-Dyson distribution. The model is the same as in Eq. (1) of the main text with $J=1$ and $h=0.5$.
• Figure 5: Relative depth for the (a) partial survival probability and (b) spin autocorrelation function vs the number of measured sites $L_s$. The chain size is $L=12$ and $\Delta_{S_P} \propto L_s^2$. The model is the same as in Eq. (1) of the main text with $J=1$ and $h=0.5$.