Regular Article

Flat-band physics in the spin-1/2 sawtooth chain

¹ Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskii Street 1, 79011 L’viv, Ukraine
² Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
³ Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
⁴ Institute of Biochemical Physics of RAS, Kosygin Street 4, 119334 Moscow, Russia
⁵ Institut für Physik, Otto-von-Guericke-Universität Magdeburg, P.O. Box 4120, 39016 Magdeburg, Germany

^a e-mail: derzhko@icmp.lviv.ua

Received: 30 April 2020
Received in final form: 5 July 2020
Published online: 24 August 2020

Abstract

We consider the strongly anisotropic spin-1/2 XXZ model on the sawtooth-chain lattice with ferromagnetic longitudinal interaction J^zz = ΔJ and aniferromagnetic transversal interaction J^xx = J^yy = J > 0. At Δ = −1∕2 the lowest one-magnon excitation band is dispersionless (flat) leading to a massively degenerate set of ground states. Interestingly, this model admits a three-coloring representation of the ground-state manifold [H.J. Changlani et al., Phys. Rev. Lett. 120, 117202 (2018)]. We characterize this ground-state manifold and elaborate the low-temperature thermodynamics of the system. We illustrate the manifestation of the flat-band physics of the anisotropic model by comparison with two isotropic flat-band Heisenberg sawtooth chains. Our analytical consideration is complemented by exact diagonalization and finite-temperature Lanczos method calculations.