Experimental observation of a quadrupolar phase via quench dynamics on a spin simulator

Recently, higher-order topological insulators have drawn much attention from researchers. For chiral-symmetric one-dimensional systems, the mean chiral displacement, a bulk observable related to the topological invariant, can distinguish topological states from trivial phases. Naturally, there exists an analogous quality for the higher-order one. In a previous work [T. Mizoguchi, Y. Kuno, and Y. Hatsugai, Phys. Rev. Lett. 126, 016802 (2021)], the mean chiral quadrupole moment is introduced. Inspired by this work, we investigate the quadrupolar phase of a higher-order topological insulator on a spin quantum simulator. With focus on a two-particle noninteracting Benalcazar-Bernevig-Hughes model, by changing the amplitude of hopping interactions, we first observe quantum phase transitions from topological phase to trivial phase using a spin simulator experimentally. Since the mean chiral quadrupole moment has robustness against environmental noise, we also test its dependence on perturbations. As an exploration of the bulk observable of a higher-order topological insulator, it may provide one path to investigate arbitrary dimensional systems.