Bound excited states of Fr\"ohlich polarons in one dimension

TL;DR

This paper predicts and characterizes multiple bound excited states of one-dimensional Fröhlich polarons at strong coupling, using numerical simulations to identify thresholds and spectral properties.

Contribution

It introduces the prediction of arbitrarily many bound excited states in the 1D Fröhlich model and demonstrates the sign problem's mitigation via walker annihilation.

Findings

Existence of multiple bound excited states at strong coupling.

Threshold for first bound excited state at 7.73 in coupling constant.

Enhanced spectral weight and phonon number at the threshold.

Abstract

The one-dimensional Fr\"ohlich model describing the motion of a single electron interacting with optical phonons is a paradigmatic model of quantum many-body physics. We predict the existence of an arbitrarily large number of bound excited states in the strong coupling limit and calculate their excitation energies. Numerical simulations of a discretized model demonstrate the complete amelioration of the projector Monte Carlo sign problem by walker annihilation in an infinite Hilbert space. They reveal the threshold for the occurrence of the first bound excited states at a value of $\alpha \approx 1.73$ for the dimensionless coupling constant. This puts the threshold into the regime of intermediate interaction strength. We find a significant spectral weight and increased phonon number of the bound excited state at threshold.