Intermediate magnetization plateaus in the spin-1/2 Ising-Heisenberg and Heisenberg models on two-dimensional triangulated lattices

TL;DR

This paper provides exact analytical and numerical results on the ground states and magnetization plateaus of spin-1/2 Ising-Heisenberg and Heisenberg models on two-dimensional triangulated lattices, revealing the role of frustration in complex magnetic behaviors.

Contribution

It offers the first exact solutions for the ground states and magnetization processes of these models, and compares classical-quantum and purely quantum results to gain insights into quantum ground states.

Findings

Multiple intermediate magnetization plateaus due to frustration.

Exact ground states include dimerized and trimerized phases.

Quantum and classical models show similar magnetization behaviors.

Abstract

The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices is exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical--quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model.