This talk aims to provide a better understanding of the role and behaviour of “doublons” (repulsively bound holes or electrons) which inevitably govern the physics of the Hubbard model in many regimes.
In the first part, the two-hole excitation spectra of the one-dimensional Hubbard model are studied for all fillings using the density-matrix renormalization group (DMRG) in combination with the Chebyshev polynomial expansion technique. Experimentally, this corresponds to Auger Electron Spectroscopy (AES). The spectra reveal what can be called “multiplon” physics, which means that the relevant final states are not only characterized by two holes (doublon), but also by three (triplon), four (quadruplon) and more; potentially forming stable compound objects or resonances with finite lifetime.
A comparison with the Bethe ansatz reveals the decay channels of the initial doublon excitation into spinons and holons in one dimension. Surprisingly, one discovers that the doublon lifetime becomes infinite at the Brillouin zone edges despite interactions. This can be traced back to the “hidden” charge-SU(2) symmetry of the Hubbard model.
In the second part, the fate of a local two-hole doublon excitation is studied in real-time. It shows a mixed ballistic-diffusive propagation through the lattice with a partial decay. The dynamics of this decay is discussed as a function of filling and interaction strength. The ambivalent role of singly occupied sites is key to understanding the time-dependent doublon physics: For high fillings, ground-state configurations with single occupancies strongly relax the kinematic constraints and open up decay channels. For fillings close to half filling, however, their presence actually helps the doublon to propagate ballistically.