Spectral function of the Holstein polaron at finite temperature

We compute the Holstein polaron spectral function on a one-dimensional ring using the finite-temperature T Lanczos method. With increasing T additional features in the spectral function emerge even at temperatures below the phonon frequency. We observe a substantial spread of the spectral weight towards lower frequencies and the broadening of the quasiparticle (QP) peak. In the weak-coupling regime the QP peak merges with the continuum in the high-T limit. In the strong-coupling regime the main features of the low-T spectral function remain detectable up to the highest T used in our calculations. The effective polaron mass shows a nonmonotonic behavior as a function of T at small phonon frequency but increases with T at larger frequencies. The self-energy remains k independent even at elevated T in the frequency range corresponding to the polaron band, while at higher frequencies it develops a distinguishable k dependence. Analytical expressions for the first few frequency moments are derived, and they agree well with those extracted from numerical calculations in a wide-T regime.