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

TL;DR

This study maps the ground-state phase diagram of an S=1/2 two-leg ladder with asymmetric leg interactions, revealing phases like ferrimagnetic, triplet-dimer, XY, and Haldane, using numerical methods.

Contribution

It introduces a comprehensive numerical analysis of the phase diagram for a frustrated two-leg ladder with different leg interactions, identifying new ground states and exact solutions.

Findings

Non-collinear ferrimagnetic state appears in frustrated regions.

Exact triplet-dimer ground state when J_{l,a}+J_{l,b}=0 and 0≤Δ≤0.83.

Phase diagrams include TD, XY, Haldane, and NCFR phases.

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.