Particles in a specific 3D lattice can form a bizarre state of matter where they stay perfectly still just to avoid touching each other.
April 24, 2026
Original Paper
The bosonic Hubbard model on a three dimensional flat band lattice
arXiv · 2604.19703
The Takeaway
Repulsive bosons in a 3D flat band lattice form exact ground states by maintaining a specific distance from one another. In most materials, particles are constantly jostling and moving, but here they organize into a rigid, non-interacting grid. This behavior causes the system entropy to drop significantly at a very specific particle density. This subextensive entropy is a hallmark of a new, strange phase of matter that doesn't follow the usual rules of thermodynamics. Understanding this state helps physicists design new quantum materials where the particles can be perfectly controlled for use in memory or processing.
From the abstract
The lowest eigenstates of the hopping matrix on the line graph of a cubic lattice with periodic boundary conditions are highly degenerate, they form a lowest flat band. Further, these states are localized. If one considers a repulsive bosonic Hubbard model on this lattice it is possible to construct exact multi-particle ground states simply by putting particles in the localized single particle ground states such that they avoid each other. This can be done up to a certain critical particle numbe