Strongly Correlated Coulomb Liquid
In typical liquids and even solids, the average interaction potential energy per particle is approximately of the same order of magnitude as the average kinetic energy. Under these conditions, the Fermi liquid approach, which reduces the many-body system
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2.1 Fundamental Correlation Functions In typical liquids and even solids, the average interaction potential energy per particle is approximately of the same order of magnitude as the average kinetic energy. Under these conditions, the Fermi liquid approach, which reduces the many-body system of strongly interacting particles to the system of weakly interacting excitations, has proven to be quite effective. On the other hand, the Coulomb liquid is characterized by extremely strong internal forces acting between electrons. This makes the conventional quasi-particle approach doubtful. As emphasized above, in the 2D Coulomb liquid of interface electrons the average interaction potential energy per electron can be approximately a hundred times larger than the average kinetic energy. One cannot rely on the Fermi liquid approach under such extreme conditions. It is even impossible to introduce a definite excitation spectrum valid for the whole Coulomb liquid if the system is subject to a normal magnetic field. In order to describe such strongly correlated electron systems, one has to use the general technique of quantum correlation functions. In Chap. 3 we shall see that the conductivity description based on the quasi-particle spectrum and kinetic equations is too detailed: in the quantum transport theory of highly correlated electrons one actually needs to know a more global property of the electron liquid, namely, the density-density correlation function or the dynamical structure factor (DSF). In this chapter we discuss the most general properties of the 2D electron liquid which originate from the strong mutual Coulomb interaction. Remarkably, we shall find that, in spite of the strong internal forces acting between electrons, the single-electron behavior remains for global properties ofthe Coulomb liquid such as the DSF S(q,w), even though the system is not equivalent to a gas-like collection of independent electrons or quasi-particles. For example, it is remarkable that in certain cases the DSF of the Coulomb liquid, and even of the Wigner solid, can be expressed in terms of a simple double integral of the DSF found for the ideal electron gas. Therefore, the use of seemingly more complicated notions and theoretical 'building blocks' such as the quantum correlation functions significantly simplifies the description of strongly interacting electron systems and reveals interesting physics. Y. Monarkha et al., Two-Dimensional Coulomb Liquids and Solids © Springer-Verlag Berlin Heidelberg 2004
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2 Strongly Correlated Coulomb Liquid
2.1.1 General Definitions In this section, we introduce some basic definitions and relations which will be used frequently throughout this book. Athough it is practically impossible to make this introduction entirely self-contained and a certain general knowledge of condensed matter theory is required of the reader, our intention is to make the following theoretical digressions as easy as possible. We shall deliberately avoid proofs of relations and identities that are quite standard and c
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