CCM Calculations For The Ground-State Properties Of The One-Dimensional Spin-Half $J_1$--$J_2$ Model: Possible Evidence of Collinear Ordering for $J_2/J_1 > \frac 12$?

TL;DR

This study uses high-order coupled cluster calculations to analyze the ground-state properties of the one-dimensional spin-half $J_1$--$J_2$ model, suggesting possible collinear ordering for $J_2/J_1 > 1/2$.

Contribution

The paper applies high-order CCM with multiple model states to explore ground-state phases and indicates potential collinear order beyond the classical transition point.

Findings

Ground-state energies favor collinear n.n.n. Néel state for $J_2/J_1 > 1/2$.

Correlation length increases with $J_2/J_1$, indicating enhanced correlations.

Structure function peak shifts from $q=\pi$ to $q=\pi/2$ as $J_2/J_1$ increases.

Abstract

In this article we investigate the linear-chain spin-half $J_1$--$J_2$ model by using high-order coupled cluster method (CCM) calculations. We employ three model states, namely, a nearest-neighbour (n.n.) N\'eel model state in which neighbouring spins are antiparallel, a next-nearest-neighbour (n.n.n.) N\'eel model state in which next-neighbouring spins are antiparallel, and finally a type of "double spiral" model state with {\it two} pitch angles. For $J_2/J_1 \le \frac 12$, we find that the n.n. N\'eel model state produces the lowest energies. For $J_2/J_1 > \frac 12$, we find that the stable states for the quantum system are those for the "traditional" spiral state in which the two pitch angles are identical and the collinear n.n.n. N\'eel model state. We show that ground-state energies for the collinear n.n.n. model state are lower than those of the spiral state in a finite region for $J_2/J_1>\frac 12$. We produce results for the dimer order parameter by using the n.n.n. N\'eel model state and these results are in reasonable agreement with previous results of DMRG. Again for the n.n.n. N\'eel model state, it is shown that the correlation length increases with increasing $J_2/J_1$ above $J_2/J_1=\frac 12$ using this model state and that shift in the peak of the structure function occurs from $q=\pi$ to $q=\pi/2$ as one increases $J_2/J_1$. Although these results are not conclusive, they are intriguing because they suggest that a ground state exhibiting collinear order might occur for some region for $J_2/J_1 \ge \frac 12$.