Temperature-dependent properties of the Holstein and of the Su–Schrieffer–Heeger polaron from the Momentum Average method

We have recently extended the Momentum Average (MA) approximation to calculate finite-temperature spectral functions of the Holstein polaron in any dimension. Our results show that the polaron effective mass increases monotonically with temperature up to the order of 0.5Ω, beyond which the quasiparticle peak merges into a broad incoherent continuum 

such that a well-defined quasiparticle peak can no longer be identified. The polaron also gains a finite lifetime and at higher temperatures, is too strongly scattered to remain a coherent excitation. These findings are in quantitative agreement with results obtained using Variational Exact Diagonalization and the Finite-Temperature Lanczos Method. Utilizing multi-site versions of the MA, we then generalized our formalism to study the finite temperature behaviour of the Su–Schrieffer–Heeger (SSH) polaron. We validate the MA results against available numerical data from Generalized Green’s function Cluster Expansion. Our work aims to advance our understanding of which aspects of finite-temperature behaviour of polarons are universal, and which are dependent on the detailed nature of the electron-phonon coupling.