Supersolid is an exotic quantum state of matter that emerges near absolute zero temperature. The spin supersolid spontaneously breaks both the lattice translational and spin rotational symmetries, forming a quantum magnetic analog of supersolid. Recently, using tensor network approaches [1,2], we determined the microscopic spin Hamiltonian of a Co-based quantum antiferromagnet Na2BaCo(PO4)2. We discovered that it represents a rare and nearly perfect realization of the easy-axis triangular lattice Heisenberg model, and therefore supports the long-sought spin supersolid state [4]. We further predict theoretically and, in conjunction with experimental collaborators, observe a significant entropic effect related to this unique and highly fluctuating spin state – spin supersolid cooling [5].

[1] B.-B. Chen, L. Chen, Z. Chen, WL, and A. Weichselbaum, Exponential thermal tensor network approach for quantum lattice models. Phys. Rev. X 8, 031082 (2018).

[2] Q. Li, Y. Gao, Y.-Y. He, Y. Qi, B.-B. Chen, and WL, Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model. Phys. Rev. Lett. 130, 226502 (2023).

[3] Y. Gao, Y. Fan, H. Li, […], Y. Wan, and WL. Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2. Npj Quantum Mater. 7, 89 (2022).

[4] J. Xiang, C. Zhang, Y. Gao, […], W. Jin, WL, P. Sun, G. Su, Giant magnetocaloric effect in spin supersolid candidate Na2BaCo(PO4)2, Nature 625, 270–275 (2024).

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