Exact degenerate ground states for the F-AF spin chain with bond alternation

TL;DR

This paper derives exact solutions for the degenerate ground states of a frustrated spin chain with bond alternation, revealing degeneracy properties on the phase boundary regardless of bond alternation parameters.

Contribution

It provides the first exact solutions for all degenerate ground states on the phase boundary of the bond-alternated $J_1$-$J_2$ spin chain, including special cases like the $ riangle$ chain.

Findings

Exact solutions for degenerate ground states are obtained.

Degeneracy persists regardless of bond alternation parameters.

Solutions include closed forms and recursion formulas.

Abstract

We investigate the $J_1$-$J_2$ spin chain consisting of spins with magnitude $\frac12$. The nearest-neighbor and the next-nearest-neighbor exchange interactions are ferromagnetic and antiferromagnetic, respectively, and induce strong frustration. Both these interactions involve the bond alternation. We find exact solutions for all the degenerate ground states on the phase boundary of the ferromagnetic phase. The degeneracy remains irrespective of two parameters representing the bond alternation. The exact solutions are of closed forms for no bond alternation and of recursion formulae in general. The exact solutions are applicable to the $\Delta$ chain as a special case.