Frustrated S = 1/2 Two-Leg Ladder with Different Leg Interactions

We explore the ground-state phase diagram of the S = 1/2 two-leg ladder. The isotropic leg interactions J_1,a and J_1,b between nearest neighbor spins in the legs a and b, respectively, are different from each other. The xy and z components of the uniform rung interactions are denoted by J_r and ΔJ_r, respectively, where Δ is the XXZ anisotropy parameter. This system has a frustration when J_1,aJ_1,b < 0 irrespective of the sign of J_r. The phase diagrams on the Δ (0≤Δ<1) versus J_1,b plane in the cases of J_1,a = − 0.2 and J_1,a = 0.2 with J_r = −1 are determined numerically. We employ the physical consideration, the level spectroscopy analysis of the results obtained by the exact diagonalization method and also the density-matrix renormalization-group method. It is found that the non-collinear ferrimagnetic (NCFR) state appears as the ground state in the frustrated region of the parameters. Furthermore, the direct-product triplet-dimer (TD) state in which all rungs form the TD pair is the exact ground state, when J_1,a + J_1,b = 0 and 0≤ Δ ≲ 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.