Incommensurability effects in odd length J_1- J_2 quantum spin chains: On-site magnetization and entanglement

摘要

For the antiferromagnetic J_1-J_2 quantum spin chain with an even number of sites, the point J_2~d = J_1/2 is a disorder point. It marks the onset of incommensurate real space correlations for J_2 > J_2~d At a distinct larger value of J_2 = 0.520 36(6)J_1, 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 J_2~d = J_1/2 but the behavior close to the Lifshitz point, J_2~L ≈ 0.5387J_1, is quite different: starting at J_2~L, 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 J_2 > 0.24 J_1 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 J_2 = J_1/2, we expect the variational results to be very precise.