Incommensurability effects in odd lengthJ1-J2quantum spin chains: On-site magnetization and entanglement

Abstract

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 ${J}_{2}^{L}=0.520\phantom{\rule{0.16em}{0ex}}36(6){J}_{1}$, the Lifshitz point, the peak in the static structure factor begins to move away from $k=\ensuremath{\pi}$. 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, ${J}_{2}^{L}\ensuremath{\simeq}0.538{J}_{1}$, is quite different: starting at ${J}_{2}^{L}$, the ground state goes through a sequence of level crossings as its momentum changes away from $k=\ensuremath{\pi}/2$. 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.