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The Effective Field Theory of Fermi Surfaces in the Vicinity of Van Hove Singularities


McKinney, Tristan James (2018) The Effective Field Theory of Fermi Surfaces in the Vicinity of Van Hove Singularities. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8VWF-V806.


The use of effective field theories to attack new and seemingly disparate problems has proliferated in the past several decades. In this thesis, we develop effective field theories for systems of fermionic quasiparticles possessing Fermi surfaces, with a particular focus on Fermi surfaces proximal to Van Hove singularities. Such systems are a fruitful source of complex and novel behavior in condensed matter physics. We begin with an overview of the renormalization group procedure at the heart of effective field theory by analyzing a simple example. We emphasize the concept that the RG relates the observables of one theory to those of another theory with precisely the same form but different numerical parameters. We also note the generality and extensibility of these concepts. We then apply this perspective to the study of quasiparticles with a round Fermi surface, employing the technique of binning the quasiparticle fields in momentum space to translate previous treatments into a more modern form. We next develop an effective field theory describing the excitations of modes around a Fermi surface with a Van Hove singularity. We resolve lingering questions about the presence of nonlocal interactions in similar models. We find a rich and complicated theory capable of describing deviations from typical Fermi liquid behavior that nonetheless displays some universal dependence on the interactions involving modes in the vicinity of the Van Hove point. We close with an analysis of the instabilities of this Van Hove effective field theory.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Effective field theory; Van Hove singularities; nonrelativistic quantum field theory; Fermi surfaces
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kapustin, Anton N.
Group:Walter Burke Institute for Theoretical Physics
Thesis Committee:
  • Kapustin, Anton N. (chair)
  • Wise, Mark B.
  • Spiropulu, Maria
  • Motrunich, Olexei I.
Defense Date:29 May 2018
Non-Caltech Author Email:tristan.j.mckinney (AT)
Record Number:CaltechTHESIS:06042018-162115007
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 4
McKinney, Tristan James0000-0003-2365-1810
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11019
Deposited By: Tristan McKinney
Deposited On:12 Jun 2018 22:15
Last Modified:04 Oct 2019 00:22

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