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

Three different tensor network 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 $\sqrt{3} \times \sqrt{3}$ state, rather than the $q = 0$ state, is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. A 1/3-magnetization plateau in the magnetic curve is observed, being consistent with the experimental observation. 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 $\sqrt{T}$ behavior, and the susceptibility approaches a finite constant as $T\rightarrow 0$. Our TN results of thermodynamic properties are compared with those from high temperature series expansion. In addition, we observe a quantum phase transition between $q = 0$ and $\sqrt{3}\times\sqrt{3}$ states in a spin-3/2 kagome XXZ model at the critical point $\Delta_c = 0.408$. This study provides reliable and useful information for further explorations on high spin kagome physics.