Path Integral of the Holstein Model with a $\phi^4$ on site potential

TL;DR

This paper derives a path integral formulation for the anharmonic Holstein model, analyzing how electron-phonon interactions and quartic on-site potentials influence thermodynamic properties, especially in low-temperature regimes.

Contribution

It introduces a novel path integral approach for the anharmonic Holstein model with quartic potentials, exploring effects in both adiabatic and antiadiabatic regimes.

Findings

Anharmonicity enhances low-energy oscillator features in thermodynamics.

Soft potentials create attractive centers affecting heat capacity.

Electron hopping induces local disorder and temperature-dependent effects.

Abstract

We derive the path integral of the semiclassical, one dimensional anharmonic Holstein model assuming that the electron motion takes place in a bath of non linear oscillators with quartic on site hard (and soft) potentials. The interplay between {\it e-ph} coupling and anharmonic force constant is analysed both in the adiabatic and antiadiabatic regime. In the latter we find much larger anharmonic features on the thermodynamic properties of low energy oscillators. Soft on site potentials generate attractive centres at large amplitude oscillator paths and contribute to the anomalous shape of the {\it heat capacity over temperature} ratio in the intermediate to low $T$ range. This anharmonic lattice effect is superimposed to the purely electronic contribution associated to a temperature dependent hopping with variable range inducing local disorder in the system.