Eur. Phys. J. B (2022) 95: 93
https://doi.org/10.1140/epjb/s10051-022-00359-0

Regular Article - Solid State and Materials

Quantum Heisenberg model on a sawtooth-chain lattice: rotation-invariant Green’s function method

¹ Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskii Street 1, 79011, L’viv, Ukraine
² Institut für Physik, Otto-von-Guericke-Universität Magdeburg, P.O. Box 4120, 39016, Magdeburg, Germany

^c derzhko@icmp.lviv.ua

Received: 3 May 2022
Accepted: 24 May 2022
Published online: 10 June 2022

Abstract

We apply the rotation-invariant Green’s function method (RGM) to study the spin $S=1/2$ 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.