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International Journal of Modern Physics B

SIGN REVERSAL OF COULOM INTERACTION BETWEEN TWO QUASIPARTICLES IN MOMENTUM SPACE

J. D. Fan, YURIY M. MALOZOVSKY

Published May 29, 2013• 2 citations
Publisher

Abstract

The main misconception regarding the interaction between quasiparticles stems from the assertion that the interaction energy between two quasiparticles is exactly identical to that of the renormalized interaction between two particles due to interparticle interaction in the Fermi system. If the main concept regarding the definition of quasiparticle as a weakly excited state of the Fermi system with conservation of charge and spin is paramount (except for the charge and spin separation models), the concept of the interaction between quasiparticles is very different from the assumption in the common sense. In this paper, we will prove a general theorem that the interaction between two quasiparticles is very much different from the renormalized interaction between two particles. The major difference lies in two places: the interaction between two quasiparticles is just negative to the renormalized interaction between two particles, and the interaction energy between the two particles is proportional to the product of two Fermi liquid renormalization factors. The result shed light on the reinterpretation of Cooper's pairing without invoking electron-photon interaction.

DOI
10.1142/s021797921362035x

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The main misconception regarding the interaction between quasiparticles stems from the assertion that the interaction energy between two quasiparticles is exactly identical to that of the renormalized interaction between two particles due to interparticle interaction in the Fermi system. If the main concept regarding the definition of quasiparticle as a weakly excited state of the Fermi system with conservation of charge and spin is paramount (except for the charge and spin separation models), the concept of the interaction between quasiparticles is very different from the assumption in the common sense. In this paper, we will prove a general theorem that the interaction between two quasiparticles is very much different from the renormalized interaction between two particles. The major difference lies in two places: the interaction between two quasiparticles is just negative to the renormalized interaction between two particles, and the interaction energy between the two particles is proportional to the product of two Fermi liquid renormalization factors. The result shed light on the reinterpretation of Cooper's pairing without invoking electron-photon interaction.
We find the singular transformation between the electron operator and the pseudoparticle operators for the Hubbard chain. We generalize the concept of quasiparticle to one-dimensional electronic systems which in 1D refers to many-pseudoparticle objects. We obtain explicit results for the electron renormalization factor, self energy, and vertex functions at the Fermi points. We also discuss the possible connection of our results to higher dimensions and explore the possibilities of instabilities in the interacting problem such as the formation of Cooper pairs.
Low-temperature properties of 3D interacting fermion systems are well described by Landau's theory of Fermi liquids; for reviews see, e.g. [183, 184]. It involves only excitations of the system around the Fermi surface on energy scales small compared to the Fermi energy. Excitations are well described by quasi-particles which are in one-to-one correspondence with the bare particles. The bare-particle interaction does not break the qualitative picture of non-interacting system, but renormalizes the dynamical characteristics (the effective mass and the pair interaction) of quasi-particles. Within the microscopic Green function formalism, the existence of quasi-particles is equivalent to assuming that the self-energy correction Σ( k , ω) is regular (has only short-range contributions in time and space) close to the Fermi surface. The lifetime of quasi-particles τ α(ε k −ε F ) −2 is long enough to consider them as well-defined eigenstates over long time-scales. The momentum occupation number of the bare particles exhibits a sharp discontinuity when crossing the Fermi momentum. The charge and spin degrees of freedom of quasi-particle always travel together. The Landau theory breaks down in 1D systems of interacting fermions which have a very specific Fermi surface consisting of two points ± k F . In such systems, the self-energy Σ( k , ω) no longer possesses the analytic properties required for introducing quasi-particles. In contrast to Fermi liquids, the momentum occupation number of the bare particles in the ground state is continuous at the Fermi momentum. Moreover, the charge and spin excitations are separated.
Spin–charge separation is considered to be one of the key properties that distinguish low-dimensional electron systems from others. Three-dimensional correlated electron systems are described by the Fermi liquid theory. There, low-energy excitations (quasiparticles) are reminiscent of noninteracting electrons: They carry charges −e and spins 1/2. It is believed that for any one-dimensional correlated electron system, low-lying electron excitations carry either only spin and no charge, or only charge without spin. That is why recent experiments looked for such low-lying collective electron excitations, one of which carries only spin, and the other carries only charge. Here we show that despite the fact that for exactly solvable one-dimensional correlated electron models there exist excitations which carry only spin and only charge, in all these models with short-range interactions the low-energy physics is described by low-lying collective excitations, one of which carries both spin and charge.
We generalize the concept of quasiparticle for one-dimensional (1D) interacting electronic systems. The \ensuremath{\uparrow} and \ensuremath{\downarrow} quasiparticles recombine the pseudoparticle colors c and s (charge and spin at zero-magnetic field) and are constituted by one many-pseudoparticle topological-momentum shift and one or two pseudoparticles. These excitations cannot be separated. We consider the case of the Hubbard chain. We show that the low-energy electron-quasiparticle transformation has a singular character which justifies the perturbative and nonperturbative nature of the quantum problem in the pseudoparticle and electronic basis, respectively. This follows from the absence of zero-energy electron-quasiparticle overlap in 1D. The existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D) many-electron systems suggests their existence in quantum liquids in dimensions 1D3. However, whether the electron-quasiparticle overlap can vanish in D>1 or whether it becomes finite as soon as we leave 1D remains an unsolved question. \textcopyright{} 1996 The American Physical Society.
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 consider a single Cooper pair with the spin dependent quasiparticle masses, with and without applied magnetic field.Such situation takes place for the strongly correlated electron systems, where a relatively strong Hubbard interaction differentiates the quasiparticle states in the majorityand the minority-spin subbands.In that situation, the two spin subbands in an applied magnetic field are not only shifted one with respect to the other, but also distorted differently, which results from the electronic correlations.Under these circumstances, the fermionic particles composing the Cooper pair, are quantum mechanically distinguishable.In result, the Cooper pair has a nonzero momentum (i.e.produces a stationary current in a similar manner as electron in the Bloch state), and there exists a critical value of the attractive interaction, below which the bound Cooper-pair state is not formed.The presence of the applied field (included via the Zeeman term) does not alter the picture qualitatively.Importance of these results for the formation of the Fulde-Ferrell-Larkin-Ovchinnikov phase in strongly correlated systems is mentioned.