Finite-temperature spectral functions of lattice polarons with process tensors

We develop a process tensor approach for calculating the finite-temperature spectral functions of lattice polarons. We show that the finite-temperature phonon influence functional can be expressed as the elementwise exponential of a low-rank matrix product state, enabling an efficient summation of electron worldlines. An embedding construction embeds worldlines of different propagation times into a single matrix product state. This construction yields the propagator over the full simulated time interval in a single calculation. We benchmark this approach against available finite-temperature density-matrix renormalization group results for the one-dimensional Holstein polaron. We further obtain numerically converged spectra for the two-dimensional Holstein polaron. The spectra reveal a progressive transfer of spectral weight from coherent spectral features into an incoherent background with increasing temperature.