Quantum magnetism studies collective phases and excitations of interacting quantum spins.
An antiferromagnetic spin wave is a long-wavelength fluctuation of staggered magnetic order. In an isotropic ordered antiferromagnet its low-energy dispersion is linear.
A ferromagnetic spin chain favors aligned neighbouring spins. Its conventional long-wavelength magnons have quadratic dispersion.
Easy-plane anisotropy penalizes spin components normal to a preferred plane, leaving a low-energy angular degree of freedom within that plane.
A ferromagnetic magnon is a quantized spin wave. Without a linear restoring term its long-wavelength frequency is proportional to .
The spin coherent-state path integral contains a Berry phase equal, modulo gauge choices, to the spin times the solid angle swept on the Bloch sphere. Single-valued path-integral amplitudes require .
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Quantum magnetism is a field of study within condensed matter physics that explores the magnetic properties and behavior of materials at the quantum level. It primarily focuses on how quantum mechanical interactions among electrons, their spins, and lattice structures lead to a variety of magnetic phenomena. In classical terms, magnetism is commonly associated with the alignment of magnetic moments (small magnetic fields due to the spin and orbital motion of electrons).