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 Delta J(r), respectively, where Delta is the XYZ anisotropy parameter. This system has a frustration when J(1,a) J(1,b) < 0 irrespective of the sign of J(r). The phase diagrams on the Delta (0 <= Delta <= 1) versus Jib plane in the cases of J(1,a) = 0.2 and L-1,L-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 <= Delta less than or similar to 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.