Family-Vicsek scaling in 1D XX Heisenberg Chains.

Family-Vicsek scaling has been thoroughly studied in classical hydrodynamics and surface dynamics. Recent reports of Kardar-Parishi-Zhang(KPZ) class scaling in XXZ Heisenberg chains demonstrate that universality classes in classical systems are also found in quantum systems [1,2]. Moreover, quantum systems can also manifest unconventional universality classes with no corresponding classical systems [3]. In this presentation, I will introduce the observation of Family-Vicsek scaling in 1D XX Heisenberg chains. We prepare a charge density wave(CDW) state within optical lattices and measure the relaxation dynamics with a quantum gas microscope. In the limit of low filling and strong on-site interactions, the Bose-Hubbard model is mapped to the XX model. We measure the relaxation dynamics for different chain lengths L=8,10,12,14,16 to extract the scaling exponents as α=0.51(3), β=0.4(1), z=1.0(1). With a digital micromirror device, we plan to impose random disorders to add decoherence to the system and investigate how the decoherence affects the scaling exponent.

[1] Ljubotina et al., Phys.Rev.Lett. 122, 210602 (2019)

[2] D. Wei et al., Science 376, 716–720 (2022)

[3] Fujimoto et al., Phys.Rev.Lett. 124, 210604 (2020)