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

TL;DR

This paper maps the ground-state phase diagram of an anisotropic S=1/2 two-leg ladder with different leg interactions, revealing various magnetic phases including a nematic TLL phase in both frustrated and unfrustrated regimes.

Contribution

The study provides the first detailed numerical phase diagram of this complex ladder system, identifying new phases and elucidating their characteristics through advanced computational methods.

Findings

Identified multiple magnetic phases including ferromagnetic, Haldane, Néel, nematic TLL, partial ferrimagnetic, and XY1.

Discovered the nematic TLL phase in both frustrated and unfrustrated strong-rung regions.

Validated phase diagram with DMRG calculations of energy gaps, local magnetization, and spin correlations.

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 $J_{{\rm l},a}$ and $\Delta_{\rm l} J_{{\rm l},a}$ ($J_{{\rm l},b}$ and $\Delta_{\rm l} J_{{\rm l},b}$). On the other hand, the $xy$ and $z$ components of the uniform rung interactions are respectively denoted by $\Gamma_{\rm r} J_{{\rm r}}$ and $J_{{\rm r}}$. In the above, $\Delta_{\rm l}$ and $\Gamma_{\rm r}$ are the $XXZ$-type anisotropy parameters for the leg and rung interactions, respectively. 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 diagram on the $\Delta_{\rm l}$ ($|\Delta_{\rm l}| \leq 1.0$) versus $J_{{\rm l},b}$ ($-2.0\leq J_{{\rm l},b}\leq 3.0$) plane in the case where $J_{{\rm l},a}=0.2$, $J_{{\rm r}}=-1.0$, and $\Gamma_{\rm r} = 0.5$ 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{\'e}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.