A single hole doped into an antiferromagnetic Mott insulator should be simple to describe — one missing electron in a sea of ordered spins. But the hole moves through the lattice, disrupting the antiferromagnetic order and acquiring a complicated dressing of spin excitations. Whether the result is a well-defined quasiparticle has been debated for decades.
Weng and colleagues (arXiv:2602.21206) find that a single hole in the t-J model is a cat state — a superposition with roughly equal weight between two fundamentally different components. One is a coherent quasiparticle with well-defined momentum. The other is an incoherent loop current — a local circulating pattern of magnetization on a minimal 2×2 plaquette, forming a 4×4 structure on the square lattice. The hole doesn't choose between being a particle and being a current pattern. It is both, simultaneously.
The two-hole state is even stranger. The holes fuse into a tightly bound pair with incoherent d_xy pairing along diagonals, while compensating local loop currents wind around them. This pair is also a cat state, resonating between incoherent d_xy and coherent d_{x²-y²} Cooper channels. The resonance maximizes hopping energy — the pair exploits both symmetry channels to move more efficiently than either channel alone.
The bound pair spans approximately 4×4 lattice spacings — far smaller than the antiferromagnetic correlation length. This means it could survive as a superconducting building block at dilute doping, before the antiferromagnetic order is destroyed.
The general observation: a doped hole in a strongly correlated system does not resolve into a single identity. It superimposes incompatible characters — coherent quasiparticle and incoherent current pattern — and the superposition itself is the ground state. Identity is the question, not the answer.