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Exactly solvable lattice models for interacting electronic insulators in two dimensions

Qing-Rui Wang Yau Mathematical Sciences Center, Tsinghua University, Haidian, Beijing 100084, China; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Huairou, Beijing 101408, China Yang Qi Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China; State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China Chen Fang Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China Meng Cheng Department of Physics, Yale University, New Haven, CT 06511-8499, USA Zheng-Cheng Gu Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

Mathematical Physics arXiv subject: High Energy Physics - Theory (hep-th) arXiv subject: Strongly Correlated Electrons (cond-mat.str-el) mathscidoc:2206.22005

2021.12
In the past decade, tremendous efforts have been made towards understanding fermionic symmetry protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is still unclear how to construct an exactly solvable model with a finite dimensional Hilbert space in general. In this paper, we give a lattice model construction and classification for 2D interacting electronic insulators. Based on the physical picture of U(1)_f-charge decorations, we illustrate the key idea by considering the well known 2D interacting topological insulator. Then we generalize our construction to an arbitrary 2D interacting electronic insulator with symmetry Gf=U(1)_f ⋊_{ρ_1,ω_2} G, where U(1)_f is the charge conservation symmetry and ρ_1,ω_2 are additional data which fully characterize the group structure of G_f. Finally we study more examples, including the full interacting classification of 2D crystalline topological insulators.
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@inproceedings{qing-rui2021exactly,
  title={Exactly solvable lattice models for interacting electronic insulators in two dimensions},
  author={Qing-Rui Wang, Yang Qi, Chen Fang, Meng Cheng, and Zheng-Cheng Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616163836210950392},
  year={2021},
}
Qing-Rui Wang, Yang Qi, Chen Fang, Meng Cheng, and Zheng-Cheng Gu. Exactly solvable lattice models for interacting electronic insulators in two dimensions. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616163836210950392.
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