Influence of the spin quantum number $s$ on the zero-temperature phase transition in the square lattice $J$-$J'$ model

TL;DR

This study explores how the spin quantum number $s$ affects the quantum phase transition in the square lattice $J$-$J'$ Heisenberg antiferromagnet, revealing that the critical coupling increases with $s$.

Contribution

It provides a comprehensive analysis of the influence of spin quantum number $s$ on the phase transition using multiple computational methods, showing a proportional relationship between $J'_c$ and $s(s+1)$.

Findings

Critical coupling $J'_c$ increases with $s$

$J'_c$ is proportional to $s(s+1)$

Transition from Néel to quantum paramagnetic phase occurs at higher $J'$ for larger $s

Abstract

We investigate the phase diagram of the Heisenberg antiferromagnet on the square lattice with two different nearest-neighbor bonds $J$ and $J'$ ($J$-$J'$ model) at zero temperature. The model exhibits a quantum phase transition at a critical value $J'_c > J$ between a semi-classically ordered N\'eel and a magnetically disordered quantum paramagnetic phase of valence-bond type, which is driven by local singlet formation on $J'$ bonds. We study the influence of spin quantum number $s$ on this phase transition by means of a variational mean-field approach, the coupled cluster method, and the Lanczos exact-diagonalization technique. We present evidence that the critical value $J'_c$ increases with growing $s$ according to $J'_c \propto s(s+1)$.