Mean field theory on the incommensurate ground state of the zigzag spin chain

Abstract

We give a mean field treatment of the incommensurate phase of the zigzag spin-1/2 Heisenberg chain containing both the nearest neighbour coupling J 1 and the next nearest neighbour antiferromagnetic coupling J 2. By use of Jordan–Wigner transformation, the zigzag spin chain is mapped into an interacting spinless fermionic system with two pairs of Fermi points. The incommensurate ground state commences when one more Fermi sea begins to be filled. The mean field theory predicts a new critical point in the ferromagnetic region x c =−2( π+1)/( π−1) such that the system is incommensurate in region x c < J 1/ J 2<2. We conjecture that the ground state in the region x c > J 1/ J 2>−4 has a nonzero total spin magnitude instead of four Fermi points.