The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field

TL;DR

This paper investigates how density-dependent magnon hopping and magnon-magnon repulsion influence the ground-state properties of ferrimagnetic spin chains in a magnetic field, using bosonic models and DMRG calculations to reveal their effects on edge states and boundary magnon densities.

Contribution

It introduces a detailed bosonic model with density-dependent hopping and magnon-magnon interactions for ferrimagnetic chains and validates it against spin model results, highlighting the impact on edge states.

Findings

Magnon-magnon repulsion raises many-magnon energy.

Density-dependent hopping reduces kinetic energy.

Edge state behavior aligns between spin and bosonic models.

Abstract

We compare the ground-state features of alternating ferrimagnetic chains $(1/2, S)$ with $S=1,3/2,2,5/2$ in a magnetic field and the corresponding Holstein-Primakoff bosonic models up to order $\sqrt{s/S}$, with $s=1/2$, considering the fully polarized magnetization as the boson vacuum. {The single-particle Hamiltonian is a Rice-Mele model with uniform hopping and modified boundaries, while the interactions have a correlated (density-dependent) hopping term and magnon-magnon repulsion.} The magnon-magnon repulsion increases the many-magnon energy and the density-dependent hopping decreases the kinetic energy. We use density matrix renormalization group calculations to investigate the effects of these two interaction terms in the bosonic model{, and display the quantitative agreement between the results from the spin model and the full bosonic approximation. In particular, we verify the good accordance in the behavior of the edge states, associated with the ferrimagnetic plateau, from the spin and from the bosonic models. Furthermore, we show that the boundary magnon density strongly depends on the interactions and particle statistics.