Quantum liquids of particles with generalized statistics

MANFRED L. RISTIG, Klaus A. Gernoth

M. V. Vavrukh, Taras Krokhmalskii

Abstract A new formalism of the statistical description of the electron liquid is proposed. The renormalized statistical perturbation theory is formulated in terms of n‐particle correlation functions of some simpler model system, called the reference system. The functional representations of the partition function, free energy, ground state energy, and two‐particle correlation function are obtained for quantum systems on the basis of the method of collective variables. The approach under consideration describes, in particular, the strongly coupled electron liquid, it is general enough and can be generalized to the case of superconducting electron systems, systems in external fields, and also Bose systems.

David L. Morabito

Kazumoto Iguchi

We discuss the quantum many-body system interacting with a separately symmetric two-body potential in higher dimensions as a generalization of the Calogero–Sutherland model in one dimension. This system exhibits the properties of a Haldane liquid such as Haldane–Wu (i.e., fractional exclusion) statistics, broken particle–hole symmetry and the existence of pseudo-Fermi surface as a generalization of the cencept of Tomonaga–Luttinger liquids in one dimension.

W. D. Kraeft, D. Kremp, W. Ebeling +1 more

Jon Magne Leinaas

We discuss how one-dimensional interacting fermion systems, which in the low-energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional charge and statistics. Our approach is to use Landau's phenomenological approach to Fermi liquid theory, where the quasiparticles are interpreted as adiabatically dressed fermions. In an earlier publication, the local charge carried by these excitations has been shown to be fractional. We focus here on the statistics of the quasiparticles and show that by a change of momentum variables the Landau parameters of the generalized Fermi fluid can be transformed to zero. This change in interaction is compensated by a change of the entropy function, which is consistent with the interpretation of the quasiparticles as satisfying generalized exclusion statistics.