Ground-State Phase Diagram of an Anisotropic S=1/2 Ladder with Different Leg Interactions

Abstract

We explore the ground-state phase diagram of the $S=1/2$ two-leg ladder with different leg interactions. The $xy$ and $z$ components of the leg interactions between nearest-neighbor spins in the $a$ ($b$) leg are respectively denoted by $J_{\mathrm{l},a}$ and ${\Delta }_{\mathrm{l}}{J}_{\mathrm{l},a}$ ($J_{\mathrm{l},b}$ and ${\Delta }_{\mathrm{l}}{J}_{\mathrm{l},b}$). On the other hand, the $xy$ and $z$ components of the uniform rung interactions are respectively denoted by ${\Gamma }_{\mathrm{r}}{J}_{\mathrm{r}}$ and $J_{\mathrm{r}}$. In the above, ${\Delta }_{\mathrm{l}}$ and ${\Gamma }_{\mathrm{r}}$ are the $XXZ$-type anisotropy parameters for the leg and rung interactions, respectively. 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 diagram on the ${\Delta }_{\mathrm{l}}$ ($|{\Delta }_{\mathrm{l}}|\le 1.0$) versus $J_{\mathrm{l},b}$ ($-2.0\le J_{\mathrm{l},b}\le 3.0$) plane in the case where $J_{\mathrm{l},a}=0.2$, $J_{\mathrm{r}}=-1.0$, and ${\Gamma }_{\mathrm{r}}=0.5$ is determined numerically. We employ the physical consideration, and the level spectroscopy and phenomenological renormalization-group analyses of the numerical date obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, N{é}el, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and $XY1$ phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated one. We perform the first-order perturbational calculations from the strong rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we make the density-matrix renormalization-group calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram.

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• Field-Induced Spin Nematic Liquid of the $S=1/2$ Bond-Alternating Chain with the Anisotropy
• Nematic Tomonaga-Luttinger Liquid Phase in an $S=1/2$ Ferromagnetic-Antiferromagnetic Bond-Alternating Chain