Anomalous behavior of the spin gap of a spin-1/2 two-leg antiferromagnetic ladder with Ising-like rung interactions

TL;DR

This paper investigates the unusual increase in the spin gap of a spin-1/2 two-leg ladder with Ising-like rung interactions near zero anisotropy, revealing a novel gap formation mechanism through numerical and perturbative analysis.

Contribution

It uncovers an anomalous gap-increasing behavior near zero anisotropy and explains its origin using degenerate perturbation theory, providing new insights into spin ladder physics.

Findings

Spin gap increases anomalously near zero anisotropy.

Different mechanisms for gap formation in positive and negative anisotropy.

Ground-state phase diagram illustrating various phases.

Abstract

Using mainly numerical methods, we investigate the width of the spin gap of a spin-1/2 two-leg ladder described by $\cH= J_\rl \sum_{j=1}^{N/2} [ \vS_{j,a} \cdot \vS_{j+1,a} + \vS_{j,b} \cdot \vS_{j+1,b} ] + J_\rr \sum_{j=1}^{N/2} [\lambda (S^x_{j,a} S^x_{j,b} + S^y_{j,a} S^y_{j,b}) + S^z_{j,a} S^z_{j,b}] $, where $S^\alpha_{j,a(b)}$ denotes the $\alpha$-component of the spin-1/2 operator at the $j$-th site of the $a (b)$ chain. We mainly focus on the $J_\rr \gg J_\rl > 0$ and $|\lambda| \ll 1$ case. The width of the spin gap as a function of $\lambda$ anomalously increases near $\lambda = 0$; for instance, for $-0.1 < \lambda < 0.1$ when $J_{\rm l}/J_{\rm r} = 0.1$. The gap formation mechanism is thought to be different for the $\lambda < 0$ and $\lambda > 0$ cases. Since, in usual cases, the width of the gap becomes zero or small at the point where the gap formation mechanism changes, the above gap-increasing phenomenon in the present case is anomalous. We explain the origin of this anomalous phenomenon by use of the degenerate perturbation theory. We also draw the ground-state phase diagram.