Observation of Ballistic and Diffusive scaling of 1D Heisenberg XX Model with Time-Dependent Potential

Dynamic scaling characterizes the fluctuations of interfaces in classical surface growth models with time. Recently, extension of the dynamical scaling to quantum system has been extensively studied using ultracold atoms [1-3]. Thanks to its powerful controllability, the investigation of transport properties can be extended into disordered, time-periodic, and open quantum systems. In this presentation, we will introduce the observation of ballistic and diffusive transport in a 1D XX Heisenberg chain in a view of the dynamic scaling. We prepared a Néel state within optical lattices and measured the time dynamics of the particles across different system sizes L=8,10,12,14,16. We then applied time-dependent “bump potentials” by addressing local potentials using the DMD (digital micromirror device) to change the transport of system. As we turned on the time-dependent potentials, we observed the diffusive scaling with exponents α=0.49(1), β=0.23(1), z=1.8(2), whereas we found ballistic scaling without exponents α=0.5(1), β=0.4(1), z=1.0(1) without time-dependent potential. Our work can be extended to study the scaling and relaxation dynamics of particles in open quantum systems and disordered systems, such as many-body localized phases.

[1] D. Wei, et al., “Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion”, Science 376, 716-720 (2022).

[2] E. Rosenberg, et al., “Dynamics of magnetization at infinite temperature in a Heisenberg spin chain”, Science 384, 48-53 (2024).

[3] J. F. Wienand, et al., “Emergence of fluctuating hydrodynamics in chaotic quantum systems”, Nat. Phys. 20, 1732–1737 (2024).

[4] J. Clayton Peacock, et al. “Many-body delocalization from embedded thermal inclusion”, Phys. Rev. B 108, L020201 (2023)