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Supersolid phase in a U(2) symmetric S = 1 magnet on the triangular lattice |
| Si-Cheng Wang(王思成)1,2,3, and Zheng-Xin Liu(刘正鑫)1,4,† |
1 Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, China;
2 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
3 University of Chinese Academy of Sciences, Beijing 100049, China 4 Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, China |
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Abstract A spin supersolid is characterized by the simultaneous breaking of lattice translation and continuous spin rotation symmetries. In this work, we study a spin-1 model with $U(2)\cong SU(2)\times U(1)/Z_2$ symmetry on the triangular lattice, and determine the phase diagram with a variational $\mathbb CP^2$ approach. We identify a novel supersolid phase which contains a 3-sublattice solid order and a superfluid order with spontaneous $SU(2)$-symmetry breaking. Unlike usual supersolid phases having only one Goldstone mode, the $SU(2)$-supersolid phase has two Goldstone modes. Another important feature of this supersolid is that the spin excitation spectrum has symmetry protected double degeneracy in the whole Brillouin zone. As by-products, several other ordered phases are obtained, including the ferromagnetic and the antiferromagnetic states breaking the $SU(2)$ symmetry, as well as genuine phases that completely break the $U(2)$ symmetry. Furthermore, the instabilities of $SU(3)$-flavor linear spin-wave theory are consistent with the phase boundaries between different ordered phases.
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Received: 24 September 2025
Revised: 07 January 2026
Accepted manuscript online: 09 January 2026
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PACS:
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75.30.Kz
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(Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.))
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75.40.Mg
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(Numerical simulation studies)
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67.80.kb
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(Supersolid phases on lattices)
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| Fund: This work was supported by the National Key Research and Development Program of China (Grant Nos. 2023YFA1406500 and 2022YFA1405300) and the National Natural Science Foundation of China (Grant Nos. 12374166 and 12134020). |
Corresponding Authors:
Zheng-Xin Liu
E-mail: liuzxphys@ruc.edu.cn
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Cite this article:
Si-Cheng Wang(王思成), and Zheng-Xin Liu(刘正鑫) Supersolid phase in a U(2) symmetric S = 1 magnet on the triangular lattice 2026 Chin. Phys. B 35 047506
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