Reaction-Matrix Theory of - Other Hard-Core Fermi Liquids

This is the first of two papers in which the binary expansion is used to study the properties of hard core fermi systems with broken gauge symmetry. In this paper, which is primarily formal, symmetry-breaking source terms are introduced into the generating function for thermodynamic quantities, and an exact expression is obtained for the generating function in terms of single-particle and two-particle sources and the reaction matrices for the two-body problem. In a subsequent paper, the theory is applied to a dilute hard sphere fluid.This is the first of two papers in which the binary expansion is used to study the properties of hard core fermi systems with broken gauge symmetry. In this paper, which is primarily formal, symmetry-breaking source terms are introduced into the generating function for thermodynamic quantities, and an exact expression is obtained for the generating function in terms of single-particle and two-particle sources and the reaction matrices for the two-body problem. In a subsequent paper, the theory is applied to a dilute hard sphere fluid.

Journal of Mathematical PhysicsMar 1, 19791 citation

THE THEORY OF A FERMI LIQUID

Elsevier eBooksJan 1, 196512 citations

Model of a two-dimensional Fermi liquid

Hamilton V. da Silveira, Marcos H. Degani, K. S. Singwi

In this paper we use a self-consistent scheme proposed by Singwi, Tosi, Land, and Sjo\ifmmode\ddot\else\textasciidieresis\fi{}lander to study a two-dimensional Fermi liquid whose particles interact via a repulsive hard-core potential with or without an attractive tail. We determine the Landau parameters ${\mathit{F}}_{0}^{\mathit{s}}$ and ${\mathit{F}}_{0}^{\mathit{a}}$ , the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential.In this paper we use a self-consistent scheme proposed by Singwi, Tosi, Land, and Sjo\ifmmode\ddot\else\textasciidieresis\fi{}lander to study a two-dimensional Fermi liquid whose particles interact via a repulsive hard-core potential with or without an attractive tail. We determine the Landau parameters ${\mathit{F}}_{0}^{\mathit{s}}$ and ${\mathit{F}}_{0}^{\mathit{a}}$, the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential.

Physical review. B, Condensed matterAug 1, 19927 citations

Strongly interacting Luttinger-liquid state in the integrable model of spinless fermions

Igor N. Karnaukhov

A family of spinless fermion models with a hard core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius. The Hamiltonian has two levels of strong interaction: the repulsive hard core potential and the kinetic energy with hopping integrals, values of which depend on the configuration of the particles. The Fermi velocity and the critical exponents describing the asymptotic behavior of the correlation functions at long distances have been calculated numerically for an arbitrary density of electrons and hard core radius. We discuss the effect of the hard core potential. The hard core potential defines an anomalous behavior of the critical exponent \ensuremath{\Theta} of the momentum distribution function. In the high-electron-density region the long-distance behavior is described by a strongly interacting Luttinger-liquid state with \ensuremath{\Theta}>1 and the residual Fermi surface disappears.A family of spinless fermion models with a hard core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius. The Hamiltonian has two levels of strong interaction: the repulsive hard core potential and the kinetic energy with hopping integrals, values of which depend on the configuration of the particles. The Fermi velocity and the critical exponents describing the asymptotic behavior of the correlation functions at long distances have been calculated numerically for an arbitrary density of electrons and hard core radius. We discuss the effect of the hard core potential. The hard core potential defines an anomalous behavior of the critical exponent \ensuremath{\Theta} of the momentum distribution function. In the high-electron-density region the long-distance behavior is described by a strongly interacting Luttinger-liquid state with \ensuremath{\Theta}>1 and the residual Fermi surface disappears.

Physical review. B, Condensed matterJan 3, 20013 citations

{\mathit{F}}_{0}^{\mathit{s}}

and

{\mathit{F}}_{0}^{\mathit{a}}

, the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential.