Statistical Properties of Strongly Correlated Quantum Liquids

Józef Spałek

Silvia Viola Kusminskiy

Józef Spałek, W. Wójcik

We propose a novel statistical-mechanical approach to a system of strongly correlated electrons in a partially filled narrow band which reproduces rigorously the situation in the atomic limit. In this approach the doubly occupied configurations are excluded both in the real and in the reciprocal spaces. Employing this principle we calculate the thermodynamic properties of those electrons. The metallic state, corresponding to a partially-filled-band case, exhibits a Fermi-liquid--type behavior at low temperatures and transforms into a spin liquid at high temperatures. This feature of our results is reminiscent of the behavior in both magnetic metals and heavy-fermion systems. Additionally, the approach reproduces correctly the statistical properties of the system of localized moments in the limit of the half-filled band, corresponding to the Mott insulating phase. These results are not obtained if one starts from the Fermi-Dirac distribution for the quasiparticles. The last assertion is reinforced by an explicit derivation of a statistical distribution function for correlated electrons which reduces to the Fermi-Dirac distribution in the limit of weak interactions, as well as to the distribution for the spin liquid derived earlier in the limit of strong correlation between the particles.

Serguei B. Isakov

Meydi Ferrier, Tomonori Arakawa, T. HATA +7 more

Klaus A. Gernoth, MANFRED L. RISTIG

Correlated Density Matrix (CDM) theory permits formal analyses of microscopic properties of strongly correlated quantum fluids and liquids at nonzero temperatures. Equilibrium properties, thermodynamic potentials, correlation and structure functions can be studied formally as well as numerically within the CDM algorithm. Here we provide the essential building blocks for studying the radial distribution function and the single-particle momentum distribution of the ingredients of the quantum systems. We focus on the statistical properties of correlated fluids and introduce the concept of renormalized bosons and fermions. These entities carry the main statistical features of the correlated systems such as liquid 4 He through their specific dependence on temperature, particle number density, and wavenumber encapsulated in their effective masses. The formalism is developed for systems of bosons and of fermions. Numerical calculations for fluid 4 He in the normal phase demonstrate the power of the renormalization concept. The formalism is further extended to analyze the Bose-Einstein condensed phases and gives a microscopic understanding of Tisza's two-fluid model for the normal and superfluid density components.