Yi J. Zhao | Searcharxiv

arXiv2026

Quantum Synchronization of Perturbed Oscillating Coherences

Quantum mutual synchronization has recently been explored through the persistent oscillation of local observables that arises from undamped eigenmodes of dissipative dynamics. However, these oscillating modes require strictly fine-tuning the system to satisfy algebraic constraints. Here, we investigate the robustness of synchronization against generic perturbations that break these constraints. We identify conditions under which the steady state of the perturbed system exhibits correlations that indicate mutual synchronization, even as the oscillations decay. That synchronization persists as imprints in the time-independent, asymptotic steady state directly bridges the dynamical notion of synchronization with the steady-state notion, which have so far been treated as distinct phenomena. Moreover, we discover in a spin-1 model that the resulting steady-state synchronization is manifested in unexpected geometries of locked phases that are multiples of $π/3$. Our work establishes a link between the two primary paradigms of quantum synchronization while demonstrating its inherent robustness against generic perturbations.

quant-ph↗

arXiv2025

Superspin Renormalization and Slow Relaxation in Random Spin Systems

We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-$\frac{1}{2}$ systems. Our formalism is suitable for systems with $\textrm{U}(1)$ and $\mathbb{Z}_2$ symmetries, and we apply it to chains of randomly positioned spins with dipolar $XX+YY$ interactions, as arise in Rydberg quantum simulators and other platforms. The formalism generates a sequence of effective Hamiltonians which provide approximate descriptions for dynamics on successively smaller energy scales. These effective Hamiltonians involve ``superspins'': two-level collective degrees of freedom constructed from (anti)aligned microscopic spins. Conserved densities can then be understood as relaxing via coherent collective spin flips. For the well-studied simpler case of randomly interacting nearest-neighbor $XX+YY$ chains, the superspins reduce to single spins. Our formalism also leads to a numerical method capable of simulating the dynamics up to an otherwise inaccessible combination of large system size and late time. Focusing on disorder-averaged infinite-temperature autocorrelation functions, in particular the local spin survival probability $\overline{S_p}(t)$, we demonstrate quantitative agreement in results between our algorithm and exact diagonalization (ED) at low but nonzero frequencies. Such agreement holds for chains with nearest-neighbor, next-nearest-neighbor, and long-range dipolar interactions. Our results indicate decay of $\overline{S_p}(t)$ slower than any power law and feature no significant deviation from the $\sim 1/ \log^2(t)$ asymptote expected from the infinite-randomness fixed-point of the nearest-neighbor model. We also apply the RSRG-X formalism to two-dimensional long-range systems of moderate size and find slow late-time decay of $\overline{S_p}(t)$.

cond-mat.dis-nn↗