We analyzed the repulsive particles in the frustrated optical lattice. For the triangular lattice, we find two co-order exist phases: supersolid [1] and ordered metals [2]. Both behave like fluid but also keep crystal structure. After introducing the spatial anisotropy, the bosonic domain walls are excited. Such topological defects can continuously change the crystal structure, so that the exotic incommensurate supersolid is observed [3]. Similar phenomena can also be found in the kagome optical lattice. When choosing cylindrical boundary condition, we found a novel edge liquid phase with fractional charges (spinons) linked by quantum strings (effective gauge field) [4]. In the strong coupling limit, we obtained the effective lattice gauge field theory which shows easy-plane NCCP1 form. And it hints the phase transition from valence bond solid to superfluid can be continuous one which is beyond Ginzburg-Landau symmetry breaking diagram. Recently, such topological phase transition is verified by utilizing large scale quantum Monte Carlo simulations [5].

[1] X.-F. Zhang, R. Dillenschneider, Y. Yu, and S. Eggert, Phys. Rev. B 84, 174515 (2011)
[2] L.-F. Tocchio, C. Gros, X.-F. Zhang, and S. Eggert, Phys. Rev. Lett. 113, 246405 (2014)
[3] X.-F. Zhang, S.-J. Hu, A. Pelster, and S. Eggert, Phys. Rev. Lett. 117, 193201 (2016)
[4] X.-F. Zhang and S. Eggert, Phys. Rev. Lett. 111, 147201 (2013)
[5] X.-F. Zhang, Y.-C. He, S. Eggert, R. Moessner, and F. Pollmann, Phys. Rev. Lett. 120, 115702 (2018)

张学锋博士于2006年山西大学物理基地班学士毕业, 2011年在中科院理论物理所获得博士学位, 之后先后在德国凯泽斯劳腾理工大学, 马克斯普朗克复杂系统物理所从事博士后研究。2017年入选重庆大学"百人计划"。主要通过量子蒙特卡洛数值模拟方法研究阻挫晶格系统中的新奇量子相, 以及相关的拓扑激发与拓扑相变。共发表《物理评论快报》6篇。