Spin-wave series for quantum one-dimensional ferrimagnets

TL;DR

This paper demonstrates that second-order spin-wave expansions accurately compute ground-state properties of quantum one-dimensional ferrimagnets, closely matching numerical methods and highlighting the effectiveness of spin-wave theory in low-dimensional quantum spin systems.

Contribution

It applies second-order spin-wave theory to quantum ferrimagnets and shows high accuracy compared to numerical methods, emphasizing its efficiency in low-dimensional systems.

Findings

Ground-state energy estimates differ less than 0.03% from DMRG calculations.

Sublattice magnetizations differ less than 0.2% from numerical results.

Spin-wave approach is highly effective for quantum ferrimagnetic chains.

Abstract

Second-order spin-wave expansions are used to compute the ground-state energy and sublattice magnetizations of the quantum one-dimensional Heisenberg ferrimagnet with nearest-neighbor antiferromagnetic interactions and two types of alternating sublattice spins $S_1>S_2$. It is found that in the extreme quantum cases $(S_1,S_2)=(1,1/2)$, $(3/2,1)$, and $(3/2,1/2)$, the estimates for the ground-state energy and sublattice magnetizations differ less than 0.03% for the energy and 0.2% for the sublattice magnetizations from the recently published density matrix renormalization group numerical calculations. The reported results strongly suggest that the quantum Heisenberg ferrimagnetic chains give another example of a low-dimensional quantum spin system where the spin-wave approach demonstrates a surprising efficiency.