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

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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 < \(J_2^{c_1}\) and J2 > \(J_2^{c_2}\) separated by a gapful quantum paramagnetic phase. We estimate \(J_2^{c_1}\)≈0.35J1 and \(J_2^{c_2}\)≈0.66J1.

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Richter, J., Schulenburg, J. The spin-1/2 J1–J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins. Eur. Phys. J. B 73, 117–124 (2010). https://doi.org/10.1140/epjb/e2009-00400-4

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