Canted spiral: An exact ground state of XXZ zigzag spin ladders

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 nonzero ordering wave vectors of the transverse spin components. We extend this result to the d=2 anisotropic triangular lattice.