Diagrammatic Monte Carlo study of the acoustic and the BEC polaron

TL;DR

This study compares the ground-state energies of BEC and acoustic polarons using Diagrammatic Monte Carlo and Feynman approaches, revealing close non-renormalized energies but notable differences in renormalized BEC polaron energies.

Contribution

It provides a detailed comparison of DiagMC and Feynman methods for polaron energies, highlighting their agreement and discrepancies in different regimes.

Findings

Both methods yield similar non-renormalized energies.

Significant discrepancies exist in renormalized BEC polaron energies.

Differences are linked to the contact interaction renormalization.

Abstract

We consider two large polaron systems that are described by a Fr\"{o}hlich type of Hamiltonian, namely the Bose-Einstein condensate (BEC) polaron in the continuum and the acoustic polaron in a solid. We present ground-state energies of these two systems calculated with the Diagrammatic Monte Carlo (DiagMC) method and with a Feynman all-coupling approach. The DiagMC method evaluates up to very high order a diagrammatic series for the polaron Green's function. The Feynman all-coupling approach is a variational method that has been used for a wide range of polaronic problems. For the acoustic and BEC polaron both methods provide remarkably similar non-renormalized ground-state energies that are obtained after introducing a finite momentum cutoff. For the renormalized ground-state energies of the BEC polaron, there are relatively large discrepancies between the DiagMC and the Feynman predictions. These differences can be attributed to the renormalization procedure for the contact interaction.