Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs

TL;DR

This paper investigates how diagonal frustrating couplings influence the quantum phase diagram of a mixed-spin two-leg ladder, revealing multiple gapped and ferrimagnetic phases through numerical and analytical methods.

Contribution

It provides a detailed characterization of the phase diagram of a mixed-spin ladder with frustration, combining numerical and effective Hamiltonian approaches, inspired by recent material synthesis.

Findings

Identification of two gapped paramagnetic phases.

Discovery of two ferrimagnetic phases with different ferromagnetic moments.

Use of density-matrix renormalization-group and exact diagonalization methods.

Abstract

We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-1/2 rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-like non-degenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-1/2 ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material Fe$^{II}$Fe$^{III}$ (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.