Electron removal spectral function of a polaron coupled to dispersive optical phonons

We explore the ground state and thermodynamic properties of the polaron coupled to quantum dispersive optical phonons in one spatial dimension. Calculations are performed using the finite--temperature Lanczos method augmented by a highly efficient construction of the variational Hilbert space. We focus on the electron removal spectral function as relevant for the angle-resolved photoemission experiments. We show that photoemission spectroscopy can be used to measure the phonon dispersion relation in a dilute system of polarons. The spectral weight of observed phonon bands is proportional to the phonon contribution to the wavefunction at finite phonon momentum. In addition, we demonstrate that when removing an electron from a polaron ground state, the polaron band does not appear in the spectral function. The latter becomes observable only at elevated temperatures.