Finite-Temperature Properties of the J1-J2 Spin-1/2 Heisenberg Antiferromagnet on the Square-Kagome Lattice

The spin-1/2 Heisenberg antiferromagnet on the kagome lattice has garnered much attention as a potential model for quantum spin liquid behavior, whereas the related square-kagome (shuriken) lattice—another geometrically frustrated arrangement of corner-sharing triangles—remains less explored. Prior studies suggest the possibility of a spin liquid ground state in this model. In this work, we investigate the finite-temperature properties of the J1-J2 spin-1/2 Heisenberg antiferromagnet on the square-kagome lattice using the finite temperature Lanczos method (FTLM) on finite-sized lattices and high-temperature series expansion (HTSE) calculations done in the thermodynamic limit. We calculate the temperature dependence of entropy, heat capacity, uniform and staggered magnetic susceptibilities, and spin-spin correlation functions to explore how finite-temperature behavior and residual low-temperature entropy reflects the underlying ground state orders as J1 and J2 vary. Our findings align with previous studies of three main ground-state phases: a Lieb ferrimagnet, a partially ordered phase of one set of spins mediated by plaquette singlets and a disordered singlet phase.