Evidence for Topological Order in the Pseudogap Metal

The violation of the Luttinger theorem in the absence of translation-symmetry breaking in the pseudogap phase of the hole-doped cuprates is a strong indication for the emergence of topological order and fractionalization. We provide further, independent evidence by showing that cluster extensions of dynamical mean-field theory and quantum Monte Carlo calculations on the strongly-correlated, hole-doped Hubbard model on the square lattice admit a natural explanation in terms of fractionalization. We study an effective low-energy model of fluctuating antiferromagnetism, exhibiting topological order and associated fractionalization of the electron’s spin and charge degrees of freedom, which already captures many essentials features found in our numerical calculations. These features include the momentum, energy, and hopping dependence of the electronic spectral function and self-energy.