Spin-ordered ground state and thermodynamic behaviors of the spin-3/2 kagome Heisenberg antiferromagnet

Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the sqrt[3]×sqrt[3] state (i.e., the state with 120^{∘} spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m/m_{s}=1/3,23/27, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a T^{2} behavior, and the susceptibility approaches a finite constant as T→0. Our TN results of thermodynamic properties are compared with those from high-temperature series expansion. In addition, we disclose a quantum phase transition between q=0 state (i.e., the state with 120^{∘} spin configuration within a unit cell containing three sites) and sqrt[3]×sqrt[3] state in a spin-3/2 kagome XXZ model at the critical point Δ_{c}=0.54. This study provides reliable and useful information for further explorations on high-spin kagome physics.