Second-order quantum corrections for the frustrated, spatially anisotropic, spin-1/2 Heisenberg antiferromagnet on a square lattice

TL;DR

This paper investigates quantum fluctuations in a frustrated, anisotropic spin-1/2 Heisenberg antiferromagnet on a square lattice, revealing how second-order quantum corrections influence phase transitions and critical points.

Contribution

It provides detailed second-order spin-wave calculations for both Neel and stripe phases, highlighting the role of quantum corrections in phase transitions and the disordered phase.

Findings

Second-order corrections significantly affect magnetization and velocities near critical points.

Quantum critical points are confirmed where magnetizations and velocities vanish.

Transitions between ordered phases are separated by a disordered paramagnetic phase.

Abstract

The effects of quantum fluctuations due to directional anisotropy and frustration between nearest neighbors and next-nearest neighbors of the quantum spin-1/2 Heisenberg antiferromagnet on a square lattice are investigated using spin-wave expansion. We have calculated the spin-wave energy dispersion in the entire Brillouin zone, renormalized spin-wave velocities, and the magnetization up to second order in 1/S expansion for the antiferromagnetic Neel and collinear antiferromagnetic stripe phases. It is shown that the second-order corrections become significant with increase in frustration. With these corrections magnetizations and spin-wave velocities for both the phases become zero at the quantum critical points as expected from other numerical and analytical methods. We have shown that the transition between the two ordered phases are always separated by the disordered paramagnetic phase.