Spectral Function of an Electron Coupled to Hard Core Bosons

TL;DR

This paper investigates the spectral properties of an electron coupled to hard core bosons, revealing a light polaron with unique spectral features and contrasting behavior to the Holstein model, especially in effective mass and bound state formation.

Contribution

It introduces a detailed analysis of electron-HCB coupling, highlighting differences from phonon-based models and demonstrating the formation of bipolaron states mediated by HCBs.

Findings

Polaron remains light even at strong coupling.

HCBs mediate attractive interactions leading to bipolaron formation.

Spectral function shows a quasiparticle band with finite lifetime near the continuum.

Abstract

The polaron, an electron dressed with HCB excitations, remains light even in the strong coupling limit as its effective mass remains of the order of the free electron mass. This result is in a sharp contrast to the Holstein model where the electron effective mass increases exponentially with the electron-phonon coupling. HCB degrees of freedom mediate the attractive potential between two electrons that form a bound singlet bipolaron state at any non-zero coupling strength. In the low-frequency regime of the electron spectral function we observe a quasi-particle (QP) band that is separated from the continuum of states only in the central part of the Brillouin zone. The quasiparticle weight approaches zero as the QP band enters the continuum where it obtains a finite lifetime. At finite temperature an electron can annihilate thermally excited HCB's. Such thermally activated processes lead to a buildup of the spectral weight below the QP band. While the investigated model bears a resemblance with the Holstein model, we point out many important differences that originate from the binary HCB excitation spectrum, which in turn mimics spin-$1\over 2$ degrees of freedom