The ground state phase diagrams and low-energy excitation of dimer XXZ spin ladder

We study the ground state and low-energy excitation of dimer XXZ spin ladder with Heisenberg and XXZ interactions along the rung and rail directions, respectively. Using a bond operator method, we get low-energy effective Hamiltonians in different parameter regions. Based on those low-energy effective Hamiltonians, we set up the ground state phase diagrams and investigate the properties of low-energy excitation in each phase. We will show that the results are exact one when the XXZ interactions along rail reduce to the Ising type. The quantum Monte Carlo and exact diagonalization methods are also applied to the finite system to verify the exact nature of the phases, the phase transitions and the low-energy excitation. 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 realized and detected by using cold atoms in optical lattice.

Graphical abstractThe ground state phases (right) of the dimer XXZ spin ladders could be realized by using cold atoms in a ladder-shaped optical lattice (left).Figure optionsDownload full-size imageDownload as PowerPoint slide