Phase Diagram of the BCS–Hubbard Model in a Magnetic Field
Dong-Hong Xu1,2†, Yi-Cong Yu1,3†, Xing-Jie Han4, Xi Chen1, Kang Wang1,2, Ming-Pu Qin5, Hai-Jun Liao1,6*, and Tao Xiang1,2,7*
1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 3Wuhan Institute of Physics and Mathematics, IAPMST, Chinese Academy of Sciences, Wuhan 430071, China 4School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China 5Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China 6Songshan Lake Materials Laboratory, Dongguan 523808, China 7Beijing Academy of Quantum Information Sciences, Beijing 100193, China
Abstract：We propose an extended BCS–Hubbard model and investigate its ground state phase diagram in an external magnetic field. By mapping the model onto a model of spinless fermions coupled with conserving $Z_2$ variables which are mimicked by pseudospins, the model is shown to be exactly solvable along the symmetric lines for an arbitrary on-site Hubbard interaction on the bipartite lattice. In the zero field limit, the ground states exhibit an antiferromagnetic order of pseudospins. In the large field limit, on the other hand, the pseudospins are fully polarized ordered. With the increase of the applied field, a first-order phase transition occurs between these kinds of phases when the on-site Coulomb interaction is less than a critical value $U_{\rm c}$. Above this critical $U_{\rm c}$, a novel intermediate phase emerges between the fully polarized and antiferromagnetic phases. The ground states in this phase are macroscopically degenerate, like in a spin ice, and the corresponding entropy scales linearly with the lattice size at zero temperature.
. [J]. 中国物理快报, 2022, 39(6): 67403-.
Dong-Hong Xu, Yi-Cong Yu, Xing-Jie Han, Xi Chen, Kang Wang, Ming-Pu Qin, Hai-Jun Liao, and Tao Xiang. Phase Diagram of the BCS–Hubbard Model in a Magnetic Field. Chin. Phys. Lett., 2022, 39(6): 67403-.
2022, Vol. 39 
