Incommensurability Effects in Odd Length J_1-J_2 Quantum Spin Chains: On-site magnetization and Entanglement

TL;DR

This paper investigates the effects of incommensurability in odd-length J_1-J_2 quantum spin chains, revealing unique ground-state behaviors, magnetization, and entanglement features near critical points using DMRG and variational methods.

Contribution

It provides new insights into the incommensurability effects and ground-state properties of odd-length J_1-J_2 chains, highlighting differences from even-length chains near critical points.

Findings

Ground-state momentum changes with J_2 near the Lifshitz point.

Significant variations in on-site magnetization and entanglement entropy for odd chains.

Distinct behavior of level crossings and ground-state wave functions in odd chains.

Abstract

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.