Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach

We develop a hierarchical equations of motion (HEOM) approach to compute real-time single-particle correlation functions and thermodynamic properties the Holstein model at finite temperature. exploit conservation total momentum system formulate momentum-space HEOM whose dynamical variables explicitly keep track exchanges between electron phonons. Our symmetry-adapted enable us overcome numerical instabilities inherent commonly used real-space HEOM. The method is then study spectral function quantities chains containing up ten sites. results compare favorably existing literature. To provide an independent assessment gain insight into importance finite-size effects, we devise quantum Monte Carlo (QMC) procedure evaluate finite-temperature in imaginary time apply it twenty QMC reveal that effects are quite weak, so on 5 10-site chains, depending parameter regime, representative larger systems. A detailed comparison data place our among reliable methods regimes ranging from low- high-temperature, weak- strong-coupling regime.