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We study the dimer $XXZ$ spin model on two-leg ladders with isotropicHeisenberg interactions on the rung and anisotropic $XXZ$ interactions alongthe rail in an external field. Combining both analytical and numerical methods,we set up the ground state phase diagram and investigate the quantum phasetransitions and the properties of rich phases, including the full polarized,singlet dimer, Luttinger liquid, triplon solid, and a non-trivialantiferromagnetic phases with gap. The analytical analyses based on solvableeffective Hamiltonians are presented for clear view of the phases andtransitions. Quantum Monte Carlo and exact diagonalization methods are employedon finite system to verify the exact nature of the phases and transitions. Ofall the phases, we pay a special attention to the gapped antiferromagneticphase, which is disclosed to be a non-trivial one that exhibits thetime-reversal symmetry. We also discuss how our findings could be detected inexperiment in the light of ultracold atoms technology advances.

Dimer XXZ Spin Ladders: Phase diagram and a Non-Trivial Antiferromagnetic Phase