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

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 $\mathcal{H}=J_{\mathrm{l},a}{\sum }_{j=1}^L{\vec{S}}_{j,a}\cdot {\vec{S}}_{j+1,a}+J_{\mathrm{l},b}{\sum }_{j=1}^L{\vec{S}}_{j,b}\cdot {\vec{S}}_{j+1,b}+J_{\mathrm{r}}{\sum }_{j=1}^L\{S_{j,a}^x{S}_{j,b}^x+S_{j,a}^y{S}_{j,b}^y+\Delta S_{j,a}^z{S}_{j,b}^z\}$. This system has a frustration when $J_{\mathrm{l},a}{J}_{\mathrm{l},b}<0$ irrespective of the sign of $J_{\mathrm{r}}$. The phase diagrams on the $\Delta$ ($0\le \Delta <1$) versus $J_{\mathrm{l},b}$ plane in the cases of {$J_{\mathrm{l},a}=-0.2$ and $J_{\mathrm{l},a}=0.2$ with $J_{\mathrm{r}}=-1$ 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 $J_{\mathrm{l},a}+J_{\mathrm{l},b}=0$ and $0\le \Delta \le 0.83$. The obtained phase diagrams consist of the TD, $XY$ and Haldane phases as well as the NCFR phase.

References in corpus (5)

• Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
• Fine-Tuning of Magnetic Interactions in Organic Spin Ladders
• Strange correlations in spin-1 Heisenberg antiferromagnets
• Ground-state phases of rung-alternated spin-1/2 Heisenberg ladder
• Ground-state phase diagram of an anisotropic S=1/2 ladder with alternating rung interactions

Cited by in corpus (5)

• Partial Ferrimagnetism in S=1/2 Heisenberg Ladders with a Ferromagnetic Leg, an Antiferromagnetic Leg, and Antiferromagnetic Rungs
• Ground-State Phase Diagram of an Anisotropic S=1/2 Ladder with Different Leg Interactions
• Nodeless $s$-Wave Superconducting Phases in Cuprates with Ba${}_2$CuO${}_3$-Type Structure
• Correlation functions at the topological quantum phase transition in the S=1 XXZ chain with single-ion anisotropy
• Frustrated plane-polarized dipoles in one dimension