Incommensurability effects in odd lengthJ1-J2quantum spin chains: On-site magnetization and entanglement
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For the antiferromagnetic J_1-J_2 quantum spin chain with an even number of
sites, the point J_2^d=1/2 J_1 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=0.52036(6)J_1, the Lifshitz point, the peak in the static
structure factor begins to move away from k=\pi. Here, we focus on chains with
an odd number of sites. In this case the disorder point is also at J_2^d=1/2
J_1, but the behavior close to the Lifshitz point, J_2^L approx. 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=\pi/2. An even length
chain, on the other hand, is gapped for any J_2>0.24J_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
bi-partite 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=1/2
J_1, we expect the variational results to be very precise.