Colorful points in the XY regime of XXZ quantum magnets

TL;DR

This paper investigates the XY regime of the XXZ quantum magnets, revealing how solvable points with exact ground states influence magnetic order and correlators, extending insights from one-dimensional models to two-dimensional lattices.

Contribution

It demonstrates the adiabatic connection of solvable points to more isotropic regimes and analyzes the projective structure of coloring ground states in 2D quantum magnets.

Findings

Solvable points influence magnetic ordering in XY regime.

Correlators computed from coloring ground states reveal static structure features.

Exact solutions exist at specific anisotropies, with some ground states surviving across regimes.

Abstract

In the XY regime of the XXZ Heisenberg model phase diagram, we demonstrate that the origin of magnetically ordered phases is influenced by the presence of solvable points with exact quantum coloring ground states featuring a quantum-classical correspondence. Using exact diagonalization and density matrix renormalization group calculations, for both the square and the triangular lattice magnets, we show that the ordered physics of the solvable points in the extreme XY regime, at $\frac{J_z}{J_\perp}=-1$ and $\frac{J_z}{J_\perp}=-\frac{1}{2}$ respectively with $J_\perp > 0$, adiabatically extends to the more isotropic regime $\frac{J_z}{J_\perp} \sim 1$. We highlight the projective structure of the coloring ground states to compute the correlators in fixed magnetization sectors which enables an understanding of the features in the static spin structure factors and correlation ratios. These findings are contrasted with an anisotropic generalization of the celebrated one-dimensional Majumdar-Ghosh model, which is also found to be (ground state) solvable. For this model, both exact dimer and three-coloring ground states exist at $\frac{J_z}{J_\perp}=-\frac{1}{2}$ but only the two dimer ground states survive for any $\frac{J_z}{J_\perp} > -\frac{1}{2}$.