Eur. Phys. J. B 31, 453-456 (2003)
https://doi.org/10.1140/epjb/e2003-00054-2

Quantum topological excitations: from the sawtooth lattice to the Heisenberg chain

¹ Département de Recherche Fondamentale sur la Matière Condensée, CEA-Grenoble/DSM 17 rue des Martyrs, 38054 Grenoble Cedex 9, France
² Laboratoire de Physique des Solides, bâtiment 510, Université Paris-Sud, 91405 Orsay Cedex, France

Corresponding authors: ^a sblundell@cea.fr - ^b nunezreg@lps.u-psud.fr

Received: 29 October 2002
Revised: 14 January 2003
Published online: 6 March 2003

Abstract

From the recently determined structure of the delafossite YCuO_2.5, we argue that the Cu-O network has nearly independent Δ chains but with different interactions between the s=1/2 spins. Motivated by this observation, we study the Δ chain for different ratios of the base-base and base-vertex interactions, . By exact diagonalization and extrapolation, we show that the elementary excitation spectrum is the same for total spins and 1, but not for , and has a gap only in the interval . The gap, known to be dispersionless for , is found to acquire increasing k-dependence as moves away from unity.