The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins

TL;DR

This paper provides exact numerical results for the ground state and low-energy excitations of the spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice with up to 40 spins, revealing phase transitions and quantum paramagnetic behavior.

Contribution

It offers the first comprehensive finite-size analysis of the J1-J2 model using exact diagonalization on large lattices, estimating critical points and characterizing phases.

Findings

Identified quantum phase transitions at J2^{c1} ≈ 0.35J1 and J2^{c2} ≈ 0.66J1.

Confirmed the existence of a gapped quantum paramagnetic phase between magnetically ordered phases.

Provided detailed estimates of ground-state energy, order parameters, and excitation gaps.

Abstract

We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N=40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J2^{c1} and J2 > J2^{c2} separated by a gapful quantum paramagnetic phase. We estimate J2^{c1} \approx 0.35J1 and J2^{c2} \approx 0.66J1.