Observing weakly broken conservation laws in a dipolar Rydberg quantum spin chain

TL;DR

This work demonstrates that weak breaking of fragile conservation laws in a dipolar XX spin chain realized with 14 Rydberg atoms leaves a measurable fingerprint on short-time quantum dynamics. By probing nonlocal observables—the variance of half-chain magnetization and a parity string operator—the authors observe rapid fluctuation growth and accelerated decay patterns that signal deviations from integrable, noninteracting behavior, even in small systems. Complementary MPS simulations for longer chains and a classical stochastic automaton reveal a consistent ballistic-to-diffusive crossover driven by backscattering processes, with a telegrapher-like continuum description emerging in the dilute limit. The study establishes nonlocal observables as sensitive probes of fragile conservation laws and provides concrete benchmarks for theories of weak integrability breaking in quantum many-body dynamics.

Abstract

Integrable quantum many-body systems host families of extensive conservation laws, some of which are fragile: even infinitesimal perturbations can qualitatively alter their dynamical constraints. Here we show that this fragility leaves a clear experimental fingerprint in a one-dimensional quantum spin chain of as few as 14 Rydberg atoms. Weak integrability breaking from interatomic dipolar couplings is directly detectable within experimentally accessible times in the dynamics of non-local observables. In particular, magnetization fluctuations are highly sensitive to the breaking of fragile conservation laws and exhibit anomalous growth, which we observe experimentally; similar signatures appear in a semilocal string observable. Numerical simulations on substantially longer chains and a simplified classical stochastic model reproduce those features. We establish non-local observables as a sensitive probe of fragile conservation laws in quantum spin chains and Rydberg-atom arrays as a platform to test perturbative descriptions of quantum many-body dynamics with weak integrability breaking.

Figures (8)

• Figure 1: Schematic overview of the 1D spin chain.a: Rydberg energy levels of a $^{87}\text{Rb}$ atom used to encode an effective spin-$1/2$. b: Fourteen atoms are arranged in a one-dimensional array with uniform spacing and initialized in a magnetic domain-wall state, defined in the text.
• Figure 2: Magnetization profile.a: Space-time map of the numerical magnetization, $\langle \hat{\sigma}^z_j\rangle(t)$, evolved under $\hat{H}_{\rm nn}+\hat{H}_{\rm nnn}$ for a chain of length $L=48$. The maximum time is chosen such that finite-size effects remain negligible. b: Ballistic rescaling of the data in a, plotting $\langle \hat{\sigma}^z_j\rangle(t)$ versus $(j-1/2)/(Jt)$; the gray region indicates the range where the collapse is observed. c: Diffusive rescaling of the data in a, plotting $\langle \hat{\sigma}^z_j\rangle(t)$ versus $(j-1/2)/(Jt)^{1/2}$. d: Space-time map of the experimental magnetization, $\langle \hat{\sigma}^z_j\rangle(t)$. e: Ballistic rescaling of the experimental data; red dots show numerical simulations for $L=14$ evolved under $\hat{H}_{\rm nn}+\hat{H}_{\rm nnn}$ over the same time window as the experiment. f: Diffusive rescaling of the experimental data, plotting $\langle \hat{\sigma}^z_j\rangle(t)$ versus $(j-1/2)/(Jt)^{1/2}$.
• Figure 3: Variance of the subsystem magnetization: space--time profile.a: Numerical space-time map of $\text{Var}[\hat{\Sigma}^z_j](t)$ for evolution under $\hat{H}_{\rm nn}+\hat{H}_{\rm nnn}$. b: Experimental space-time map of $\text{Var}[\hat{\Sigma}^z_j](t)$ after post-processing (see text).
• Figure 4: Variance of the half-chain magnetization.a: Numerical simulations of $\text{Var}[\hat{\Sigma}^z_{j=0}]$ under Hamiltonian evolution with $\hat{H}_{\rm nn}$ and with $\hat{H}_{\rm nn} +\hat{H}_{\rm nnn}$; the chain has length $L=48$. b: Difference between the two curves shown in a. c, d and e: Experimental data for $\Delta \text{Var}[\hat{\Sigma}^z_j]$ for several values of $j$ after postprocessing (see the text), and comparison with $\text{Var}[\hat{\Sigma}^z_{j=0}]$ for the integrable $\hat{H}_{\rm nn}$ and the non-integrable $\hat{H}_{\rm nn}+\hat{H}_{\rm nnn}$. f: Sketch of the backscattering processes induced by Hamiltonian $\hat{H}_{\rm nnn}$: a pair of fermionic quasiparticles $(k_1,k_2)$ can be turned into a coherent superposition of pairs of particles propagating in opposite directions, $(k_1,k_2)$ and $(k'_1,k'_2)$; eventually they will be on the two different halves of the system, $j\leq 0$ or $j>0$, and let $\hat{\Sigma}^z_{j=0}$ develop important quantum fluctuations.
• Figure 5: String operator.a and b: Numerical space-time profiles of $\langle \hat{P}^z_j \rangle(t)$ for evolution under $\hat{H}_{\rm nn}$ and $\hat{H}_{\rm nn}+\hat{H}_{\rm nnn}$, respectively. c: Experimental space-time profile of $\langle \hat{P}^z_j \rangle(t)$. d and e: Numerical time traces of $\langle \hat{P}^z_{j = 0} \rangle(t)$ for evolution under $\hat{H}_{\rm nn}$ and $\hat{H}_{\rm nn}+\hat{H}_{\rm nnn}$, respectively. f: Experimental data for $\langle \hat{P}^z_{j = 0} \rangle(t)$, rescaled to start from $1$.