Flat-band physics in the spin-1/2 sawtooth chain
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Flat-band physics in the spin-1/2 sawtooth chain Oleg Derzhko 1,2,a , J¨ urgen Schnack 3 , Dmitry V. Dmitriev 4 , Valery Ya. Krivnov 4 , and Johannes Richter 2,5 1
2 3 4 5
Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskii Street 1, 79011 L’viv, Ukraine Max-Planck-Institut f¨ ur Physik komplexer Systeme, N¨ othnitzer Straße 38, 01187 Dresden, Germany Fakult¨ at f¨ ur Physik, Universit¨ at Bielefeld, Postfach 100131, 33501 Bielefeld, Germany Institute of Biochemical Physics of RAS, Kosygin Street 4, 119334 Moscow, Russia Institut f¨ ur Physik, Otto-von-Guericke-Universit¨ at Magdeburg, P.O. Box 4120, 39016 Magdeburg, Germany Received 30 April 2020 / Received in final form 5 July 2020 Published online 24 August 2020 c The Author(s) 2020. This article is published with open access at Springerlink.com
Abstract. We consider the strongly anisotropic spin-1/2 XXZ model on the sawtooth-chain lattice with ferromagnetic longitudinal interaction J zz = ∆J and aniferromagnetic transversal interaction J xx = J yy = J > 0. At ∆ = −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.
1 Introduction Frustrated quantum Heisenberg spin systems are of great interest nowadays. Exact calculations and rigorous statements, although scarce, are obviously important for this field. One source of such results stems from the flat-band antiferromagnets, i.e., the models with a dispersionless (flat) one-magnon band [1]. The flat one-magnon band leads to localized multi-magnon states which dominate the low-temperature physics in antiferromagnetic flat-band models close to the saturation field. Their contribution to the partition function can be exactly calculated by visualizing the localized multi-magnon states as hardcore-object configurations on a corresponding auxiliary lattice. Then the hard-core description allows to use classical statistical mechanics to describe frustrated quantum spin models. This approach has been successfully used for a wide class of frustrated quantum antiferromagnets supporting flat bands [2–7] including the kagome antiferromagnet in two dimensions and the pyrochlore antiferromagnet in three dimensions. We mention that a similar description of flat-band states can be developed for the Hubbard model [1,8–12]. A popular one-dimensional example of a flat-band antiferromagnet is the Heisenberg sawtooth chain with the special rel
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