Fractional magnetization plateaux of the spin-1/2 Heisenberg orthogonal-dimer chain revisited: strong-coupling approach developed from the exactly solved Ising-Heisenberg model

TL;DR

This paper develops a strong-coupling perturbative approach based on an exactly solvable model to analyze fractional magnetization plateaux and quantum phases in the spin-1/2 Heisenberg orthogonal-dimer chain, achieving results consistent with numerical methods.

Contribution

The paper introduces a second-order strong-coupling perturbation theory from the exactly solvable Ising-Heisenberg model to study magnetization plateaux in the Heisenberg orthogonal-dimer chain, revealing new fractional plateaux and quantum phases.

Findings

Confirmation of the one-third fractional plateau.

Identification of a gapless Luttinger spin-liquid phase.

Excellent agreement with numerical data from ED and DMRG.

Abstract

The spin-1/2 Heisenberg orthogonal-dimer chain is considered within the perturbative strong-coupling approach, which is developed from the exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with the Heisenberg intradimer and the Ising interdimer couplings. Although the spin-1/2 Ising-Heisenberg orthogonal-dimer chain exhibits just intermediate plateaux at zero, one-quarter and one-half of the saturation magnetization, the perturbative treatment up to second order stemming from this exactly solvable model additionally corroborates the fractional one-third plateau as well as the gapless Luttinger spin-liquid phase. It is evidenced that the approximate results obtained from the strong-coupling approach are in an excellent agreement with the state-of-the-art numerical data obtained for the spin-1/2 Heisenberg orthogonal-dimer chain within the exact diagonalization and density-matrix renormalization group method. The nature of individual quantum ground states is comprehensively studied within the developed perturbation theory.