Frustrated S=1/2 Two-Leg Ladder with Different Leg Interactions (1608.02064v2)

Abstract: We explore the ground-state phase diagram of the $S!=!1/2$ two-leg ladder with different isotropic leg interactions and uniform anisotropic rung ones, which is described by the Hamiltonian ${\cal H}=J_{{\rm l},a} \sum\nolimits_{j=1}^{L}{\vec S}{j,a}\cdot {\vec S}{j+1,a}+J_{{\rm l},b} \sum\nolimits_{j=1}^{L} {\vec S}{j,b}\cdot {\vec S}{j+1,b}+J_{\rm r} \sum\nolimits_{j=1}^{L} \bigl{S_{j,a}^x S_{j,b}^x + S_{j,a}^y S_{j,b}^y + \Delta S_{j,a}^z S_{j,b}^z \bigr}$. This system has a frustration when $J_{{\rm l},a} J_{{\rm l},b}!<!0$ irrespective of the sign of $J_{\rm r}$. The phase diagrams on the $\Delta$ ($0!\leq!\Delta!<!1$) versus $J_{{\rm l},b}$ plane in the cases of {$J_{{\rm l},a}!=!-0.2$ and $J_{{\rm l},a}!=!0.2$ with $J_{{\rm r}}!=!-1$ 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 $J_{{\rm l},a}!+!J_{{\rm l},b}!=!0$ and $0 \leq \Delta \leq 0.83$. The obtained phase diagrams consist of the TD, $XY$ and Haldane phases as well as the NCFR phase.