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

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.

Latest version to be published in Phys. Rev. B. enlarged to around 40 pages

References in corpus (10)

• Bosonization and Fermion Liquids in Dimensions Greater Than One
• Bosonization of the Low Energy Excitations of Fermi Liquids
• Bosonization of Fermi liquids
• Dynamical correlation functions in the Calogero-Sutherland model
• Bosonization of interacting fermions in arbitrary dimension beyond the Gaussian approximation
• On the Stability and Single-Particle Properties of Bosonized Fermi Liquids
• Fock Representations of Quantum Fields with Generalized Statistic
• Bosonization of Fermi Systems in Arbitrary Dimension in Terms of Gauge Forms
• Calogero-Sutherland Type Models in Higher Dimensions
• Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models

Cited by in corpus (8)

• Calculus of Sea-Displacement Operators
• Bosonization and Quantum Hydrodynamics
• Sea-Boson Theory of Landau Fermi Liquids, Luttinger Liquids and Wigner Crystals
• U(1) Gauge Theory as Quantum Hydrodynamics
• A General Approach to Bosonization
• Expressing the Field Operator in Terms of Currents and Densities
• Exact Optical Dielectric Function of a Nearly Homogeneous Solid
• Fermi-Bose Correspondence at Finite Temperature