Abstract
We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.
Highlights
Spin ladders play an important role in quantum magnetism
We show that the transition between two different ground states which occurs for an isolated rung survives in a spin ladder and dominates its behavior
We show that the transition between the two above ground states in an isolated rung survives in a spin ladder with AFM Ising interactions along the legs [20], N
Summary
Spin ladders play an important role in quantum magnetism. Interest in them over the last two decades is motivated by their numerous experimental realizations in transition metal oxides [1]. Excitation spectra of such AFM spin ladders are rich and were understood only in the last decade They consist of triplet excitation, bound states and two-particle continuum [4], and were calculated in unprecedented detail for quantum AFM spin 1/2 two-leg ladder employing optimally chosen unitary transformation [5]. The orbital interactions are frequently Ising-like but different spin components interact depending on the bond orientation in real space [15], which generates frustrated interactions in the so-called two-dimensional (2D) quantum compass model. This model was investigated numerically [16,17,18], while its 1D variant was solved exactly by an analytic method [9].
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