Phase diagram of the frustrated, spatially anisotropic S=1 antiferromagnet on a square lattice

TL;DR

This study investigates the phase diagram of a frustrated S=1 antiferromagnetic square lattice, revealing a quantum disordered phase connecting isotropic and decoupled Haldane chains, emphasizing the importance of quantum fluctuations.

Contribution

It combines DMRG and SBMFT methods to show that quantum fluctuations stabilize a disordered phase across all anisotropies, challenging semiclassical predictions.

Findings

Quantum disordered phase exists for all anisotropies.

The paramagnetic phase connects to decoupled Haldane chains.

Quantum fluctuations are essential in S=1 frustrated systems.

Abstract

We study the S=1 square lattice Heisenberg antiferromagnet with spatially anisotropic nearest neighbor couplings $J_{1x}$, $J_{1y}$ frustrated by a next-nearest neighbor coupling $J_{2}$ numerically using the density-matrix renormalization group (DMRG) method and analytically employing the Schwinger-Boson mean-field theory (SBMFT). Up to relatively strong values of the anisotropy, within both methods we find quantum fluctuations to stabilize the N\'{e}el ordered state above the classically stable region. Whereas SBMFT suggests a fluctuation-induced first order transition between the N\'{e}el state and a stripe antiferromagnet for $1/3\leq J_{1x}/J_{1y}\leq 1$ and an intermediate paramagnetic region opening only for very strong anisotropy, the DMRG results clearly demonstrate that the two magnetically ordered phases are separated by a quantum disordered region for all values of the anisotropy with the remarkable implication that the quantum paramagnetic phase of the spatially isotropic $J_{1}$-$J_{2}$ model is continuously connected to the limit of decoupled Haldane spin chains. Our findings indicate that for S=1 quantum fluctuations in strongly frustrated antiferromagnets are crucial and not correctly treated on the semiclassical level.