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arXiv:cond-mat/9609210 · Journal of Physics Condensed Matter

Non-Fermi liquids in the extended Hubbard model

Qimiao Si A

Published Nov 25, 1996• 7 citations
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Abstract

I summarize recent work on non-Fermi liquids within a certain generalized Anderson impurity model as well as in the large-dimensionality (D) limit of the two-band extended Hubbard model. The competition between local charge and spin fluctuations leads either to a Fermi liquid with renormalized quasiparticle excitations, or to non-Fermi liquids with spin - charge separation. These results provide new insights into the phenomenological similarities and differences between different correlated metals. While presenting these results, I outline a general strategy of local approach to non-Fermi liquids in correlated electron systems.

DOI
10.1088/0953-8984/8/48/019

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I summarize recent work on non-Fermi liquids within a certain generalized Anderson impurity model as well as in the large-dimensionality (D) limit of the two-band extended Hubbard model. The competition between local charge and spin fluctuations leads either to a Fermi liquid with renormalized quasiparticle excitations, or to non-Fermi liquids with spin - charge separation. These results provide new insights into the phenomenological similarities and differences between different correlated metals. While presenting these results, I outline a general strategy of local approach to non-Fermi liquids in correlated electron systems.
We study an extended Hubbard model in the limit of infinite dimensions. The local correlation functions of this model are those of a generalized asymmetric Anderson model. The impurity model displays a Fermi liquid phase, a phase with neither the spin nor the charge of the impurity quenched, and an intermediate phase with the spin but not the charge of the impurity quenched. This analysis establishes the existence of metallic non-Fermi-liquid phases of the lattice model over a wide range of parameters and electron densities. The non-Fermi-liquid phases describe metals with incoherent spin and/or charge excitations and self-similar local correlation functions.
We study the non-Fermi liquid behavior in a two-band extended Hubbard model. In the limit of infinite dimensions, where only local correlations are taken into account, this model in the mixed-valence regime is known to display a metallic non-Fermi liquid phase with spin-charge separation. Here we address the effect of intersite RKKY-like interactions using an extended dynamical mean-field approach. We find that the spin-charge separation survives the quantum fluctuations associated with the intersite density-density and spin-exchange interactions. We determine the spin, charge, and single-particle correlation functions in the non-Fermi liquid state.
We study an extended Hubbard model in the limit of infinite dimensions and its zero-dimensional counterpart, a generalized asymmetric Anderson model. In the impurity model we find three kinds of mixed valence states: (a) the usual strong-coupling state in which a resonance forms at the Fermi level; (b) a weak-coupling state in which neither the impurity spin nor the impurity charge degrees of freedom are quenched; and (c) an intermediate-coupling state where the spin but not the charge degree of freedom is quenched. The corresponding phases of the extended Hubbard model in infinite dimensions are (a) a Fermi liquid; (b) a non-Fermi-liquid state with incoherent charge and spin excitations; and (c) a non-Fermi-liquid state with incoherent charge but coherent spin excitations. The non-Fermi-liquid phases are incoherent metallic states with vanishing quasiparticle residue, self-similar local correlation functions, and asymptotically decoupled charge and spin excitations. The non-Fermi-liquid phases occur for a wide range of parameters.
We summarize recent theoretical results of our group concerning the electronic states of the strongly correlated fermions at nonzero temperature. The state of almost localized fermions is discussed within a mean-field approach for auxiliary bosons, both in the narrow-band (Section 2) and in the hybridized band (Section 3) cases. This state represents a metallic state of correlated fermion systems (such as V{sub 2}O{sub 3}) below the Mott-Hubbard localization threshold. The Fermi liquid state does not describe properly the properties of narrow band electrons in the large Hubbard -- U limit beyond the localization threshold. Therefore, in Section 4 and 5 we introduce a phenomenological concept of statistical spin liquid which describes principal features of a crossover from a high-temperature superconductor to the Mott insulator for a two-dimensional system. It also reproduces the main features of the phase diagram for La{sub 2-x}Sr{sub x}CuO{sub 4} system, which is modelled by a planar structure.
We study the effects of intersite RKKY-like interactions in the mixed valence regime of a two-band extended Hubbard model. This model is known to display a metallic non-Fermi liquid state with spin-charge separation in the standard D=∞D=\inftyD=∞ limit (where interactions lead to purely on-site fluctuations only). Using an extended D=∞D=\inftyD=∞ approach, we find that the spin-charge separation survives the quantum fluctuations associated with arbitrary intersite density-density interactions and a finite range of intersite spin-exchange interactions. We determine the qualitative behavior of the spin, charge, and single-particle correlation functions. The implications of these results for the solution in finite spatial dimensions are discussed.
Strongly correlated electron systems show a rich variety of interesting physical phenomena. However, their theoretical description poses a highly non-trivial task, and even the simplest models cannot be solved exactly. In this thesis the intricate behavior of the single impurity Anderson model (SIAM) and the Hubbard model is investigated. The main emphasis is laid on two-particle Green functions of these systems. To this end, existing approximation schemes are extended to be capable of treating susceptibilities as well. The quality and range of applicability of these approximations is discussed in detail. The physical pictures behind the phenomena encountered in these systems are introduced. A prominent many-body effect is the emergence of temperature dependent low energy quasiparticles in both models. The occurrence of such excitations is a result of the dynamical screening of local magnetic moments, a characteristic feature of the Kondo effect. It is argued, that within the presented approximations, the low temperature phase of these models can usually be described as a Fermi liquid. As a counterexample, the Hubbard model is shown to exhibit pronounced non-Fermi liquid behavior in situations, where a van Hove singularity in the non-interacting density of states is found in the vicinity of the Fermi level. The magnetic properties of the Hubbard model are discussed in view of the two archetypical pictures of magnetism: local moment magnetism and itinerant Stoner-magnetism. Critical temperatures for antiferromagnetic, ferromagnetic and incommensurate phase transitions are calculated, and the influence of the lattice structure and frustration is examined. In strongly correlated metallic situations, the complicated competition between Kondo-screening and local moment magnetism can lead to a reentrant behavior of the N\'eel temperature. A direct signature of the Kondo effect in the Hubbard model is found in the dynamic magnetic susceptibility, where a localized collective mode emerges at very low temperatures. It is connected to the breakup of a singlet formed by the local moments with their Kondo-screening cloud, and consequently the excitation energy is of the order of the low energy scale T*.