Journal
ANNALS OF PHYSICS
Volume 326, Issue 3, Pages 541-565Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2010.09.011
Keywords
Renormalization group theory; Ionization energy theory; Energy-level spacing; Electron-electron and electron-phonon interactions; Quantum phase transitions; Screened Coulomb potential; Dielectric functions; Heat capacity and Debye frequency
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Funding
- Slovene Human Resources Development and Scholarship Fund (Ad-Futura)
- Slovenian Research Agency (ARRS)
- Institut Jozef Stefan (IJS)
- School of Physics, University of Sydney
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Proofs are developed to explicitly show that the ionization energy theory is a renormalized theory, which mathematically exactly satisfies the renormalization group formalisms developed by Cell-Mann-Low, Shankar and Zinn-Justin. However, the cutoff parameter for the ionization energy theory relies on the energy-level spacing, instead of lattice point spacing in k-space. Subsequently, we apply the earlier proofs to prove that the mathematical structure of the ionization-energy dressed electron-electron screened Coulomb potential is exactly the same as the ionization-energy dressed electron-phonon interaction potential. The latter proof is proven by means of the second-order time-independent perturbation theory with the heavier effective mass condition, as required by the electron-electron screened Coulomb potential. The outcome of this proof is that we can derive the heat capacity and the Debye frequency as a function of ionization energy, which can be applied in strongly correlated matter and nanostructures. (C) 2010 Elsevier Inc. All rights reserved.
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