Upper bound of one-magnon excitation and lower bound of effective mass for ferromagnetic spinor Bose and Fermi gases

TL;DR

This paper derives exact bounds on one-magnon excitation energies and effective mass corrections in ferromagnetic spinor gases, applicable to both Bose and Fermi systems in various dimensions, using a variational approach.

Contribution

It provides the first exact upper bounds for one-magnon excitation energies and effective mass limits in ferromagnetic spinor gases, encompassing both Bose and Fermi systems.

Findings

Upper bound for one-magnon excitation energy in ferromagnetic spinor gases.

Positive quantum correction limit for magnon effective mass.

Bounds applicable to lattice and continuum systems in multiple dimensions.

Abstract

Using a variational method, we derive an exact upper bound for one-magnon excitation energy in ferromagnetic spinor gases, which limits the quantum corrections to the effective mass of a magnon to be positive. We also derive an upper bound for one-magnon excitation energy in lattice systems. The results hold for both Bose and Fermi systems in $d$ dimensions as long as the interaction is local and invariant under spin rotation.