Excitations of a low-dimensional dimerized spin ladder under a magnetic field

TL;DR

This paper investigates the magnetic excitations and magnetization plateaus in a dimerized spin ladder with competing interactions under a magnetic field, revealing conditions for various plateau states and phase transitions.

Contribution

It predicts new magnetization plateau states influenced by spin-Peierls interactions and analyzes phase transitions in a dimerized spin ladder system.

Findings

Existence of multiple magnetization plateaus depending on dimerization and anisotropy.

Identification of a saturation plateau corresponding to a classical phase.

Numerical support for the analytical predictions from existing literature.

Abstract

We study the dimerized spin ladder with nearest-neighbor ($J_1$) and next-nearest-neighbor ($J_2$) anti-ferromagnetic interaction under a magnetic field. We predict the existence of different magnetization plateaus for the presence of spin-Peierls interaction on both $J_1$ and $J_2$. Magnetization plateau at $m=0$ for $J_1$ dimerization is spontaneous due to XY interaction, but it is absent for $J_2$ dimerization, only intrinsic umklapp term leads to plateau (spin gap) state for some specific values of XXZ anisotropy ($\Delta$) and $J_2$. Here we predict a saturation plateau which is the classical phase of the system. There are some numerical support of our analytical approach already existing in the literature. The transition from commensurate gapped phase to incommensurate Luttinger liquid phase is the Mott-$\delta$ type of transition.