The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study

TL;DR

This study examines the ground-state magnetic phases of the spin-1/2 J1-J2 Heisenberg model on a square lattice with ferromagnetic J1 and antiferromagnetic J2, using advanced numerical methods to identify phase transition points and compare with antiferromagnetic J1 cases.

Contribution

The paper provides high-precision estimates of the transition point where ferromagnetic order vanishes in the J1-J2 model with ferromagnetic J1, using coupled-cluster and exact diagonalization methods, and compares these with the antiferromagnetic J1 case.

Findings

Transition point at J2^{c1} ≈ 0.394|J1| for ferromagnetic J1

Similar behavior between ferromagnetic and antiferromagnetic J1 models at large J2

No evidence of an intermediate disordered phase near J2 ≈ 0.4|J1| for ferromagnetic J1

Abstract

We investigate the ground-state magnetic order of the spin-1/2 J1-J2 Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange J2>0. We use the coupled-cluster method to high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N=40 sites in order to calculate the ground-state energy, the spin-spin correlation functions, and the magnetic order parameter. We find that the transition point at which the ferromagnetic ground state disappears is given by J2^{c1}=0.393|J1| (exact diagonalization) and J2^{c1}=0.394|J1| (coupled-cluster method). We compare our results for ferromagnetic J1 with established results for the spin-1/2 J1-J2 Heisenberg model with antiferromagnetic J1. We find that both models (i.e., ferro- and antiferromagnetic J1) behave similarly for large J2, although significant differences between them are observed for J2/|J1| \lesssim 0.6. Although the semiclassical collinear magnetic long-range order breaks down at J2^{c2} \approx 0.6J1 for antiferromagnetic J1, we do not find a similar breakdown of this kind of long-range order until J2 \sim 0.4|J1| for the model with ferromagnetic J1. Unlike the case for antiferromagnetic J1, if an intermediate disordered phase does occur between the phases exhibiting semiclassical collinear stripe order and ferromagnetic order for ferromagnetic J1 then it is likely to be over a very small range below J2 \sim 0.4|J1|.