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

Abstract

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

4 pages, REVTex, 6 figures in eps-files uuencoded

References in corpus (4)

• DMRG Studies of the Spin-Half Heisenberg System with Dimerization and Frustration
• Elementary excitations in the $\Delta$-chain
• On Quantum Solitons in the Sawtooth Lattice
• Density Matrix Renormalization Group Study of the Spin 1/2 Heisenberg Ladder with Antiferromagnetic Legs and Ferromagnetic Rungs

Cited by in corpus (7)

• Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds
• Enhancement of magnetization plateaus in low dimensional spin systems
• Localization length of a soliton from a non-magnetic impurity in a general double-spin-chain model
• Magneto- and barocaloric properties of the ferro-antiferromagnetic sawtooth chain
• Haldane and dimer gap in general double spin-chain models
• Behavior of a frustrated quantum spin chain with bond dimerization
• Antikink dispersions of the $J_1$-$J_2$ sawtooth spin-1/2 anisotropic Heisenberg antiferromagnetic chain