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

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