Universality classes, statistical exclusion principle, and properties of interacting fermions.

We point to the possibility of existence of the statistical-spin-liquid state as the state which differs from either Fermi or Luttinger liquid states. In the statistical spin liquid the double occupancies are excluded from the physical space. Each of the above three cases (Fermi, Luttinger and spin liquids) represents an universality class for the interacting many-particle fermion systems. The properties of the spin liquid such as the chemical potential, the entropy, and the magnetization curve, as well as the quasiparticle structure are briefly discussed. PACS Nos. 05.30.-d, 71.10.+x, 71.27.+a, 71.30.+h Typeset using REVTEX ∗E-mail: [email protected], [email protected] 1 In the theory of correlated systems the principal problem is to transform the microscopic model of interacting particles into an effective approach with interaction among quasiparticles and/or collective excitations. Haldane [1] in his seminal paper provided an unified framework of the effective theory of interacting fermions in a normal (metallic) state. The Fermi surface, whose existence is a basic postulate of the approach, is considered as a d-1 dimensional collection of points, where the momentum distribution function nk has singularities. Obviously, this might be either a step discontinuity (as in the Fermi liquid case), or any weaker singularity (as in the case of Luttinger liquid). The Fermi surface in both cases must obey the Luttinger theorem which is taken as an additional postulate. Starting from these two postulates one can describe the low-energy long-wave-length excitations of the system solely in terms of the fluctuating Fermi surface. Explicitly, one introduces the local Fermi wave vector kFQσ(x) related to the undistorted Fermi wave vector kFQσ(x) by kFQσ(x) = k 0 FQσ(x) + δkFQσ(x), (1) where vector Q with d-1 components, where d is the space dimension, describes a coarsegrained point of the Fermi surface, σ = ±1 is the spin quantum number, and x is a position variable. It turns out [1] that only normal to the surface fluctuations δk (‖) FQσ(x) give contributions to the physical quantities such as the local fluctuation in the total particle density, which is defined as δnσ(x) = ∑