Abstract.
Magnetism is often introduced through explicit spin–spin interactions, such as the exchange coupling in the Heisenberg model. However, magnetic correlations can also arise purely from the motion of charge carriers.
In this lecture, I will use the infinite-U Hubbard model with a single mobile hole to illustrate this idea. I will first explain the Nagaoka mechanism, i.e. that a ferromagnetic spin background allows the hole to move coherently and thereby minimise its kinetic energy.
However, lattice geometry can obstruct this motion. This effect, known as kinetic frustration, occurs when a hole cannot optimise its motion around all loops of a lattice simultaneously. I will show how in kinetically frustrated models, hole motion instead favour antiferromagnetic spin correlations, an effect known as the counter-Nagaoka mechanism.
On certain frustrated lattices, the counter-Nagaoka mechanism can stabilise an exotic quantum state in which neighbouring spins form singlets, and the full state is a quantum superposition of all possible singlet coverings. This is known as a resonating-valence-bond (RVB) liquid. Using the checkerboard lattice as an example, I will derive a rigorous lower bound on the energy and show that the RVB wavefunction saturates this bound, making it an exact ground state. Along the way, we will see how lattice geometry, strong interactions, and fermionic quantum statistics can produce unconventional magnetic states from kinetic energy alone.
(The slides are be available here)