Free Fermion System Research Articles

THE CORNER TRANSFER MATRIX OF SOME FREE-FERMION SYSTEMS AND MEIXNER’S POLYNOMIALS

Corner transfer matrices of some free-fermion vertex systems on a finite lattice, are exactly diagonalised in the Hamiltonian limit with the help of a special class of orthogonal polynomials: the Meixner polynomials. We present the derivation, discuss the asymptotic behavior for a large lattice and compare the results with numerical computation.

Fay's trisecant identity and conformal field theory

We study the correlation functions of a system of free chiral fermions on a compact Riemann surface using techniques of algebraic geometry. Fay's trisecant identity arises as a consequence of the proof of the uniqueness of correlation functions.

Conformal embeddings and hidden symmetries of free fermion theories

It is shown that the conformal field theory of free complex fermions transforming in the (anti)symmetric tensor representation R of u( N) is characterized by a nontrivial operator algebra. However, this theory can be naturally embedded into the theory of free Dirac fermions in the defining representation of u(dim R); the latter theory corresponds to an operator algebra which is trivial in the sense that e.g. φ×φ + = 1 . We argue that these observations can be generalized to any system of free fermions possessing an energy-momentum tensor of the Sugawara form. As a consequence, there exist no further cases where a free fermion theory is quantum equivalent to a WZW theory, besides the ones already well known (i.e. those based on the current algebras so (N) and u ̂ (N) with unit central charge).

Fermion propagator and composite-boson propagators on random lattices

The ensemble averages of various propagators of a free-fermion system on random lattices in D = 1 and D = 2 are calculated numerically. The results indicate a correct continuum limit. The cancellation mechanism of the unphysical states is investigated.

Spins and fermions on arbitrary lattices

It is proved that the system of free fermions on arbitrary lattices is equivalent to the set of locally interacting constrained spins. The fermionic counterpart of the unconstrained spin system is also derived. The generalization to the interacting theories is possible.

The exact solution for two interacting systems of free fermions

Abstract The hamiltonian of the free fermion system is determined as a quadratic form of classical fermion fields. Two systems of free fermions connected by the four-particle interaction were considered. The exact solution for the free energy model is obtained.

Recent advances in the theory of superconductivity

The theory of superconductivity in which it is assumed that there is a net attractive interaction between pairs of electrons in time-reversed ststes, which give rise to a condensed stste in which electrons near the Fermi surface are strongly correlated over distances of approximately 1O/sup -4/cm, is reviewed. The excitation modes and a generalized enengy gap equation are discussed. A system of free fermions interacting via an effective two-body potential whose matrix elements are attractive for transitions in which both particles remain in the region about the Fermi surface but are repulsive otherwise is considered. The application of the independent quasi-particle approximation to a system of fermions interacting via strong short-range forces is also discussed. (M.C.G.)