Journal of Experimental and Theoretical Physics

, Volume 127, Issue 5, pp 826–843 | Cite as

Fermi-Liquid Theory and Pomeranchuk Instabilities: Fundamentals and New Developments

  • A. V. ChubukovEmail author
  • A. Klein
  • D. L. Maslov


This paper is a short review on the foundations and recent advances in the microscopic Fermi-liquid (FL) theory. We demonstrate that this theory is built on five identities, which follow from conservation of the total charge (particle number), spin, and momentum in a translationally and SU(2)-invariant FL. These identities allow one to express the effective mass and quasiparticle residue in terms of an exact vertex function and also impose constraints on the “quasiparticle” and “incoherent” (or “low-energy” and “high-energy”) contributions to the observable quantities. Such constraints forbid certain Pomeranchuk instabilities of a FL, e.g., towards phases with order parameters that coincide with charge and spin currents. We provide diagrammatic derivations of these constraints and of the general (Leggett) formula for the susceptibility in arbitrary angular momentum channel, and illustrate the general relations through simple examples treated in perturbation theory.



We thank J. Schmalian, P. Woelfle, and Y. Wu for valuable discussions. The work was supported by NSF DMR-1523036 (A. V. C. and A. K.) and NSF DMR-1720816 (D. L. M.).


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Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Department of Physics, University of MinnesotaMinneapolisUSA
  2. 2.Department of Physics, University of Florida, P. O. Box 118440GainesvilleUSA

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