One- and two-dimensional spin systems in the regime close to deconfinement of spinons

Abstract

Based on the Majumdar-Ghosh chain we construct several spin models which allow us to investigate spinon dynamics in the regime close to deconfinement of spinons. We consider the $J_1{-J}_2-\delta$ model, two coupled $J_1{-J}_2$ chains (ladder), and a two-dimensional array of coupled $J_1{-J}_2$ chains. Using the picture of two spinons interacting with a string confining potential we calculate the singlet-triplet splitting, magnetic structure factor, tunneling amplitude of two spinons, and the excitation spectra for the ladder and the array.