Incommensurability effects in odd length J1-J2 quantum spin chains: On-site magnetization and entanglement

For the antiferromagnetic J1-J2 quantum spin chain with an even number of sites, the point J2d=J1/2 is a disorder point. It marks the onset of incommensurate real space correlations for J2>J2d. At a distinct larger value of J2L=0.52036(6)J1, the Lifshitz point, the peak in the static structure factor begins to move away from k=π. Here, we focus on chains with an odd number of sites. In this case, the disorder point is also at J2d=J1/2 but the behavior close to the Lifshitz point, J2L≃0.538J1, is quite different: starting at J2L, the ground state goes through a sequence of level crossings as its momentum changes away from k=π/2. An even length chain, on the other hand, is gapped for any J2>0.24J1 and has the ground-state momentum k=0. This gradual change in the ground-state wave function for chains with an odd number of sites is reflected in a dramatic manner directly in the ground-state on-site magnetization as well as in the bipartite von Neumann entanglement entropy. Our results are based on DMRG calculations and variational calculations performed in a restricted Hilbert space defined in the valence bond picture. In the vicinity of the point J2=J1/2, we expect the variational results to be very precise.