Variational Studies of Triangular Heisenberg Antiferromagnet in Magnetic Field

TL;DR

This paper uses variational methods and exact diagonalization to explore the phase diagram of the anisotropic triangular Heisenberg antiferromagnet in a magnetic field, identifying various coplanar, non-coplanar, and quasi-1D states.

Contribution

It introduces accurate variational wavefunctions for the 1/3-magnetization plateau and nearby phases, extending understanding of phase competition in anisotropic triangular lattices.

Findings

Identification of stable coplanar and non-coplanar phases across anisotropy levels.

Validation of variational wavefunctions through exact diagonalization.

Discovery of quasi-1D physics dominance at high anisotropy.

Abstract

We present a variational study of the Heisenberg antiferromagnet on the spatially anisotropic triangular lattice in magnetic field. First we construct a simple yet accurate wavefunction for the 1/3-magnetization plateau uud phase on the isotropic lattice. Beginning with this state, we obtain natural extensions to nearby commensurate coplanar phases on either side of the plateau. The latter occur also for low lattice anisotropy, while the uud state extends to much larger anisotropy. Far away from the 1/3 plateau and for significant anisotropy, incommensurate states have better energetics, and we address competition between coplanar and non-coplanar states in the high field regime. For very strong anisotropy, our study is dominated by quasi-1d physics. The variational study is supplemented by exact diagonalization calculations which provide a reference for testing the energetics of our trial wavefunctions as well as helping to identify candidate phases.