Thermal and quantum lattice fluctuations in Peierls chains

TL;DR

This study investigates the thermodynamic and spectral behavior of electrons coupled to quantum phonons in Peierls chains using quantum Monte Carlo simulations, revealing how polaron formation and phonon renormalization influence specific heat and spectral properties.

Contribution

It provides accurate thermodynamic data across all electron-phonon couplings and phonon frequencies, and introduces an efficient estimator for the specific heat within the spinless Holstein model.

Findings

Polaron excitations significantly affect the specific heat.

Phonon mode renormalization occurs across the Peierls transition.

Results validate Tomonaga-Luttinger liquid theory in this context.

Abstract

The thermodynamic and spectral properties of electrons coupled to quantum phonons are studied within the spinless Holstein model. Using quantum Monte Carlo simulations, we obtain accurate results for the specific heat and the compressibility, covering the entire range of electron-phonon couplings and phonon frequencies. To this end, we derive an efficient estimator for the specific heat using the properties of the perturbation expansion. This allows us to quantitatively test the predictions of Tomonaga-Luttinger liquid theory as well as the widely used adiabatic approximation for low phonon frequencies. A comparison with the spectral functions of electrons and phonons reveals that the formation of polaron excitations as well as the renormalization of the phonon mode across the Peierls transition have a pronounced effect on the specific heat in the adiabatic regime.