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arXiv:hep-th/9706006 · Physical review. B, Condensed matter

Single-particle Green functions in exactly solvable models of Bose and Fermi liquids

Girish S. Setlur, Yia-Chung Chang

Published Jun 15, 1998• 17 citations
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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, is the random-phase approximation in its many guises recovered in the Fermi case, and Bogoliubov's theory in the Bose case. The momentum distribution is evaluated using two different approaches, exact diagonalization and the equation of motion approach; the novelty being, of course, the exact computation of single-particle properties including short-wavelength behavior.

DOI
10.1103/physrevb.57.15144

Related papers

Reply to “Comment on ‘Single-particle Green functions in exactly solvable models of Bose and Fermi liquids’ ”

Girish S. Setlur, Yia-Chung Chang

It is shown that the sea-boson model given in G.S. Setlur and Y.C. Chang, Phys. Rev. B 57, 15 144 (1998), is capable of reproducing the four-point correlation functions of fermion operators within the random-phase approximation, although an explicit expression for the sea-boson operator is still lacking.

Physical review. B, Condensed matter•Sep 15, 1999•2 citations

Comment on “Single-particle Green functions in exactly solvable models of Bose and Fermi liquids”

L. C. Cune, Marian Apostol

It is shown that the construction introduced recently by Setlur and Chang [Phys. Rev. B 57, 15 144 (1998)] for generalized Fermi sea-displacement operators contains undefined elements, which may lead to divergencies, and, in fact, these operators are not bosonic operators, in contrast to what these authors claim.

Physical review. B, Condensed matter•Sep 15, 1999•3 citations

Exact Dynamical Structure Factor of a Bose Liquid

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Based on ideas introduced in a previous preprint cond-mat/9701206 we propose an exactly solvable model of bosons interacting amongst themselves via a Van-der Waal-like repulsive interaction, and compute both the filling fraction and the dynamical structure factor exactly. The novelty of this approach involves introducing, analogous to Fermi sea (or surface) displacements, Bose fields that in this case, correspond to fluctuations of the Bose condensate. The exact dynamical structure factor has a coherent part that corresponds to the Bogoliubov spectrum and an incoherent part that is a result of correlations.

arXiv:cond-mat/9704222•Apr 27, 1997•1 citation

Expressing Products of Fermi Fields in terms of Fermi Sea Displacements

Girish S. Setlur

An attempt is made to generalise the ideas introduced by Haldane and others regarding Bosonizing the Fermi surface. The present attempt involves introduction of Bose fields that correspond to displacements of the Fermi sea rather than just the Fermi surface. This enables the study of short wavelength fluctuations of the Fermi surface and hence the dispersion of single particle excitations with high energy. The number conserving product of two Fermi fields is represented as a simple combination of these Bose fields. It is shown that most(!) commutation rules involving these number conserving products are reproduced exactly, as are the dynamical correlation functions of the free theory. Also the work of Sharp, Menikoff and Goldin has shown that the field operator may be viewed as a unitary representation of the current algebra. An explicit realisation of this unitary representation is given in terms of canonical conjugate of the density operator.

arXiv:cond-mat/9701206•Jan 29, 1997•3 citations

Improved Theory of Single-Particle Properties Using Sea-bosons

Girish S. Setlur

In this article, we combine the ideas introduced by us earlier in various proportions to arrive at a simple and yet powerful means of studying single-particle properties of homogeneous Fermi systems in detail without making assumptions regarding the validity or otherwise of Fermi-liquid theory. Novelties include the exact forms of the momentum distribution and spectral functions in the intermediate density regime and a dielectric function that is sensitive to significant qualitative changes in single-particle properties. This time, care is taken to include the particle-hole mode by interpreting the sum over modes as a weighted sum with the dynamical structure factor appearing as the weight.

arXiv:cond-mat/0001326•Jan 21, 2000•0 citations

Exact spectral functions of a non-Fermi liquid in one dimension

Karlo Penc, B. Sriram Shastry

We study the exact one-electron propagator and spectral function of a solvable model of interacting electrons due to Schulz and Shastry. The solution previously found for the energies and wave functions is extended to give spectral functions that turn out to be computable, interesting, and nontrivial. They provide one of the few examples of cases where the spectral functions are known asymptotically as well as exactly.

arXiv:cond-mat/0109339•Physical review. B, Condensed matter•Mar 29, 2002•8 citations
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, is the random-phase approximation in its many guises recovered in the Fermi case, and Bogoliubov's theory in the Bose case. The momentum distribution is evaluated using two different approaches, exact diagonalization and the equation of motion approach; the novelty being, of course, the exact computation of single-particle properties including short-wavelength behavior.
Based on ideas introduced in a previous preprint cond-mat/9701206 we propose an exactly solvable model of bosons interacting amongst themselves via a Van-der Waal-like repulsive interaction, and compute both the filling fraction and the dynamical structure factor exactly. The novelty of this approach involves introducing, analogous to Fermi sea (or surface) displacements, Bose fields that in this case, correspond to fluctuations of the Bose condensate. The exact dynamical structure factor has a coherent part that corresponds to the Bogoliubov spectrum and an incoherent part that is a result of correlations.
An attempt is made to generalise the ideas introduced by Haldane and others regarding Bosonizing the Fermi surface. The present attempt involves introduction of Bose fields that correspond to displacements of the Fermi sea rather than just the Fermi surface. This enables the study of short wavelength fluctuations of the Fermi surface and hence the dispersion of single particle excitations with high energy. The number conserving product of two Fermi fields is represented as a simple combination of these Bose fields. It is shown that most(!) commutation rules involving these number conserving products are reproduced exactly, as are the dynamical correlation functions of the free theory. Also the work of Sharp, Menikoff and Goldin has shown that the field operator may be viewed as a unitary representation of the current algebra. An explicit realisation of this unitary representation is given in terms of canonical conjugate of the density operator.
In this article, we combine the ideas introduced by us earlier in various proportions to arrive at a simple and yet powerful means of studying single-particle properties of homogeneous Fermi systems in detail without making assumptions regarding the validity or otherwise of Fermi-liquid theory. Novelties include the exact forms of the momentum distribution and spectral functions in the intermediate density regime and a dielectric function that is sensitive to significant qualitative changes in single-particle properties. This time, care is taken to include the particle-hole mode by interpreting the sum over modes as a weighted sum with the dynamical structure factor appearing as the weight.