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

2 , 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.