Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids

TL;DR

This paper provides exact calculations of single-particle Green functions in solvable models of Bose and Fermi liquids, covering all wavelengths and dimensions, and connects these results to established approximations like RPA and Bogoliubov theory.

Contribution

It introduces a method to compute single-particle propagators exactly in all dimensions for Bose and Fermi liquids, reducing spectral functions to quadratures and linking to known theories.

Findings

Exact spectral functions are obtained for all wavelengths and dimensions.

The approach recovers RPA and Bogoliubov theory in appropriate limits.

Momentum distributions are computed via two independent methods.

Abstract

Based on a class of exactly solvable models of interacting bose and fermi liquids, we compute the single-particle propagators of these systems exactly for all wavelengths and energies and in any number of spatial dimensions. The field operators are expressed in terms of bose fields that correspond to displacements of the condensate in the bose case and displacements of the fermi sea in the fermi case. Unlike some of the previous attempts, the present attempt reduces the answer for the spectral function in any dimension in both fermi and bose systems to quadratures. It is shown that when only the lowest order sea-displacement terms are included, the random phase approximation in its many guises is recovered in the fermi case, and Bogoliubov's theory in the bose case. The momentum distribution is evaluated using two different approaches, exact diagonalisation and the equation of motion approach. The novelty being of course, the exact computation of single-particle properties including short wavelength behaviour.