Relaxation of frustration and gap enhancement by the lattice distortion in the $Δ$ chain

Abstract

We clarify an instability of the ground state of the $Δ$ chain against the lattice distortion that increases a strength $(λ)$ of a bond in each triangle. It relaxes the frustration and causes a remarkable gap enhancement; only a $6\%$ increase of $λ$ causes the gap doubled from the fully-frustrated case $(λ=1)$. The lowest excitation is revealed to be a kink-antikink bound state whose correlation length decreases drastically with $λ$ increase. The enhancement follows a power law, $ΔE_{\rm gap}\sim (λ-1) + 1.44 (λ-1)^{\frac{2}{3}}$, which can be obtained from the exact result of the continuous model. This model describes a spin gap behavior of the delafossite YCuO$_{2.5}$.