Strongly interacting fermion systems: Emphasis on heavy fermions

Ulf-G. Meißner

K. Yamada

Heavy fermion systems are explained on the basis of the Fermi liquid theory. The specific heat, magnetic susceptibility and electrical resistivity are discussed. Using Anderson's orthogonality theorem, we show that the Fermi liquid is nothing but a local spin singlet state at every site. Heavy fermion systems The Fermi liquid theory is independent of a model Hamiltonian, and can be applied to any system as long as the system remains a Fermi liquid. The theory tells us that even if the electron interaction becomes strong, physical quantities behave as those of the non-interacting Fermi gas. The difference between them with and without interaction is not qualitative but quantitative. As seen at the Mott transition in Hubbard systems, the effective mass of the electron increases near the transition point. As a system realizing such a large effective mass, a Fermi liquid system called the heavy electron system or the heavy fermion system attracts general interest. The heavy fermion systems are composed of the rare earth metals such as Ce and Yb, and actinide atoms such as U. The heavy fermions are nothing but the quasi-particles in the Fermi liquid theory. As a quasi-particle in a strongly correlated electron system, the heavy fermion is an important issue to be studied in the development of the Fermi liquid theory. The heavy fermion realized in f -electron systems is one of the heavy quasi-particles appearing near the Mott transition.

Alma Bardon, Lindsay J. LeBlanc, M. Extavour +4 more

Achim Rosch

In this review, a detailed discussion of the behaviour of a heavy particle interacting with a Fermi sea is given. Particular emphasis is put on the issue of how strong correlations influence coherence and transport of the particle. First, we investigate the question of whether the heavy particle is a well defined quasiparticle at low temperatures. While in one dimension ( D = 1) and at a van Hove singularity in D = 2 the coherence of the particle is destroyed, the quasiparticle weight is finite in higher dimensions. The most important transport quantity is the diffusion constant or mobility of the heavy particle. We are able to describe both the well known high-temperature properties and the cross-over to the lowest temperatures in a unified approximation scheme based on a self-consistent evaluation of an effective action. Two strong-correlation effects of independent origin are discussed. The first arises if the scattering of the fermions from the heavy particle is nearly resonant, that is, if one of the scattering phase shifts δ is close to π/2. In this regime an anomalous exponent is observed in the temperature dependence of the mobility μ(T). In D = 3, for instance, the mobility is proportional to T-3/2 rather than to T-2. The second effect is a giant mass renormalization in the case of a large particle. In this situation, the low-temperature effective mass M* increases up to an exponentially large value, M* exp[c(r/λF)3], where r is the effective radius of the particle, λF the Fermi wavelength and c a non-universal constant of order one.

M. A. Contínentino

Abstract The theory of quantum critical phenomena is introduced to study some current many-body problems in condensed matter physics. Renormalization group concepts are applied to strongly correlated electronic materials which are close to a zero-temperature instability. These systems have enhanced effective masses and susceptibility. Scaling arguments yield the exponents which govern the critical behavior of these quantities in terms of the usual critical exponents associated with a zero-temperature phase transition. We show the existence of a new energy scale, related to the quantum nature of the many-body instability, which can be generally associated with the setting of Fermi-liquid behavior with decreasing temperature in three-dimensional strongly interacting electronic systems. The theory of quantum critical phenomena is used to investigate the Kondo lattice problem, which provides a model to describe heavy-fermion systems and to introduce a scaling theory of the Mott transition with special emphasis on charge fluctuation effects. However, this report is not a review on heavy fermions and Mott insulators. The microscopic theories of these systems are still controversial and present some of the most challenging and instigating problems in condensed matter physics. This state of affairs stimulated the author to review and extend the scaling approach. The scaling theory we develop provides a powerful tool, based on the notion of universality, to understand the physical properties of correlated systems beyond the mean-field level. This is illustrated by our treatment of the one-dimensional Hubbard model, where, although the Fermi-liquid fixed point does not survive the fluctuations, the scaling approach is still useful. Finally, we discuss briefly how disorder affect our results.

José M. Arias, María Isabel Gallardo, Manuel Lozano