Abstract

The spin-1/2 Ising-Heisenberg model on diamond-like decorated Bethe lattices is exactly solved in the presence of the longitudinal magnetic field by combining the decoration-iteration mapping transformation with the method of exact recursion relations. In particular, the ground state and low-temperature magnetization process of the ferrimagnetic version of the considered model is investigated in detail. Three different magnetization scenarios with up to two consecutive fractional magnetization plateaus were found, whereas the intermediate magnetization plateau may either correspond to the classical ferrimagnetic spin arrangement and/or the field-induced quantum ferrimagnetic spin ordering without any classical counterpart.

Highlights

  • Low-dimensional quantum spin systems have attracted much attention over the past few decades, since they exhibit a lot of striking quantum phenomena including fractional magnetization plateaus, spin-Peierls dimerization, unconventional spin-liquid ground states, or many other peculiar valencebond-solid ground states such as the Haldane phase [1, 2]

  • Exact solution for the investigated model has been obtained by combining the decoration-iteration mapping transformation with the method of exact recursion relations

  • Exact results for the partition function, Gibbs free energy, total and both sublattice magnetizations were derived by making use of this rigorous approach

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Summary

Introduction

Low-dimensional quantum spin systems have attracted much attention over the past few decades, since they exhibit a lot of striking quantum phenomena including fractional magnetization plateaus, spin-Peierls dimerization, unconventional spin-liquid ground states, or many other peculiar valencebond-solid ground states such as the Haldane phase [1, 2]. From the theoretical point of view, an exact treatment of the quantum Heisenberg model remains an unresolved problem mainly due to substantial mathematical difficulties, which arise from a noncommutability of spin operators involved in the relevant Hamiltonian. This mathematical complexity can be avoided by considering simpler Ising-Heisenberg models, which describe hybrid classical-quantum spin systems constituted both by the ‘classical’ Ising as well as the quantum Heisenberg spins. Bethe lattice with the effective nearest-neighbour interaction and the effective magnetic field Owing to this precise mapping correspondence, exact on the diamond-like decorated.

Ising-Heisenberg model on decorated Bethe lattices
Results and discussion
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