Exact Degenerate Ground States for the F–AF Spin Chain with Bond Alternation

Abstract

We investigate the J₁–J₂ spin chain consisting of spins with magnitude 1/2. The nearest-neighbor and 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 at the phase boundary of the ferromagnetic phase. The degeneracy remains irrespective of the two parameters representing the bond alternation. The exact solutions are of recursion formulae in general and of closed forms for no bond alternation in the nearest-neighbor interaction. The exact solutions are applicable to the Δ chain as a special case.