Gapless Spin Liquid and Nonlocal Corner Excitation in the Spin-$1/2$ Heisenberg Antiferromagnet on Fractal
Haiyuan Zou1* and Wei Wang2
1Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China 2Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
Abstract：Motivated by the mathematical beauty and the recent experimental realizations of fractal systems, we study the spin-$1/2$ antiferromagnetic Heisenberg model on a Sierpiński gasket. The fractal porous feature generates new kinds of frustration to exhibit exotic quantum states. Using advanced tensor network techniques, we identify a quantum gapless-spin-liquid ground state in fractional spatial dimension. This fractal spin system also demonstrates nontrivial nonlocal properties. While the extremely short-range correlation causes a highly degenerate spin form factor, the entanglement in this fractal system suggests a long-range scaling behavior. We also study the dynamic structure factor and clearly identify the gapless excitation with a stable corner excitation emerged from the ground-state entanglement. Our results unambiguously point out multiple essential properties of this fractal spin system, and open a new route to explore spin liquid and frustrated magnetism.
Zou H, Cui Y, Wang X, Zhang Z, Yang J, G X, Okutani A, Hagiwara M, Matsuda M, Wang G, Mussardo G, Hódsági K, Kormos M, Z H, Kimura S, Yu R, Yu W, Ma J, and Wu J 2021 Phys. Rev. Lett.127 077201
2023, Vol. 40 
