Exact dimer phase with anisotropic interaction for one dimensional magnets

Abstract

We report the exact dimer phase, in which the ground states are described by product of singlet dimer, in the extended XYZ model by direct generalizing the isotropic Majumdar-Ghosh model to the fully anisotropic regime. This model also supports three different ferromagnetic (FM) phases, denoted as x-FM, y-FM and z-FM. The boundaries between the dimer phase and FM phases are infinite-fold degenerate. The breaking of this infinite-fold degeneracy by either translational symmetry or Z2 symmetry lead to dimer phase and FM phases, respectively. Moreover, the boundaries between the three FM phases are critical with central charge c = 1. We characterize the properties of these boundaries using entanglement entropy, excitation gap and long-range spin-spin correlations. These results are relevant to a large number of quasi-one-dimensional magnets, in which anisotropy is necessary to isolate a single chain out from the bulk material. We discuss the possible experimental signatures in true materials with magnetic field along different directions, and show that the anisotropy may resolve the long-standing disagreements between theory and experiments.

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field*

“…LiInCr 4 O 8 was found to be spin-3/2 breathing pyrochlore antiferromagnet, which is an alternating array of small and large tetrahedra [10]. Recently, it is reported that the results from the dimer anisotropic XYZ model are relevant to a large number of quasi-one dimensional magnets [11]. In history, Bulaevskii predicted that a spin gap exists in the nonuniform antiferromagnetic (AFM) spin chains [12].…”