Phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice

TL;DR

This study uses exact diagonalization to map the phase diagram of the spin-1/2 J1-J2-J3 Heisenberg model on a square lattice, revealing quantum fluctuations' significant impact and discovering new quantum phases.

Contribution

It provides a detailed numerical analysis of the phase diagram, highlighting the role of quantum fluctuations and identifying new quantum phases beyond classical predictions.

Findings

Quantum fluctuations alter the extent and wave vector of classical spiral phases.

Discovery of a new phase with small or vanishing spin-stiffness.

Identification of additional quantum phases such as valence-bond-solid and bond-nematic.

Abstract

We presents the results of an extensive numerical study of the phase diagram of the spin-1/2, \protect{$J_1$-$J_2$-$J_3$} Heisenberg model on a square lattice, for both ferromagnetic and antiferromagnetic nearest-neighbor interactions $J_1$, using exact diagonalization with periodic and twisted boundary conditions. Comparison is made with published spin wave calculations. We show that quantum fluctuations play a very important role, changing both the extent and the wave vector of classical spiral phases, and leading to new quantum phases where the classical spiral states have a high degeneracy. These include a new phase with small or vanishing spin-stiffness, in addition to known valence-bond-solid and bond-nematic phases.