The spectral function of Mott-insulating Hubbard ladders: From fractional excitations to coherent quasi-particles

We study the spectral function of two-leg Mott insulating Hubbard ladders using the time-dependent density matrix renormalization group method (tDMRG). The spectrum displays features of both spin-charge separation and coherent bound states. As the inter-leg hopping is increased, both spin and hole branches merge into a single coherent quasi-particle band and the spectrum undergoes a crossover from a regime with two incommensurate minima, to one with a single minimum. At the same time, the system shifts from a Mott insulator to a band insulator. Interestingly, while the bonding sector of the spectrum realizes quasi-particles, the anti-bonding one displays a broad low energy scattering continuum, which can be associated to the lack of quasi-particles. We identify the processes leading to quasiparticle formation by studying the time evolution of charge and spin degrees of freedom in real space after a hole is created. At short times, incoherent holons and spinons are emitted but charge and spin quickly form polarons that propagate coherently.