The Canted Spiral: An Exact Ground State of XXZ Zigzag Ladders

TL;DR

This paper derives exact ground states for a family of XXZ zigzag ladder models, revealing long-range spiral order with a ferromagnetic component, and extends the findings to a 2D triangular lattice.

Contribution

It provides the first exact solutions for the ground states exhibiting spiral order in XXZ zigzag ladders and extends the analysis to two-dimensional lattices.

Findings

Exact ground states with spiral order derived

Spiral order breaks U(1) symmetry in 1D

Results extended to 2D triangular lattice

Abstract

We derive the exact ground states for a one dimensional family of $S=1/2$ XXZ Hamiltonians on the zigzag ladder. These states exhibit true long range spiral order that spontaneously breaks the U(1) invariance of the Hamiltonian. Besides breaking a continuous symmetry in $d=1$, this spiral ordering has a ferromagnetic component along the symmetry axis that can take any value between zero and full saturation. In this sense, our canted spiral solutions are a generalization of the SU(2) Heisenberg ferromagnet to non-zero ordering wave-vectors of the transverse spin components. We extend this result to the $d=2$ anisotropic triangular lattice.