Quantum Heisenberg model on a sawtooth-chain lattice: Rotation-invariant Green's function method

We apply the rotation-invariant Green’s function method (RGM) to study the spin $S=1\mathrm{/}2$ Heisenberg model on a one-dimensional sawtooth lattice, which has two nonequivalent sites in the unit cell. We check the RGM predictions for observable quantities by comparison with the exact-diagonalization and finite-temperature-Lanczos calculations. We discuss the thermodynamic and dynamic properties of this model in relation to the mineral atacamite Cu${}_2$Cl(OH)${}_3$ complementing the RGM outcomes by results of other approaches.