Controlled access to the low-energy physics of critical Fermi surfaces

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Condensed matter physics is the study of the complex behaviour of a large number of interacting particles such that their collective behaviour gives rise to emergent properties. We will discuss some interesting quantum condensed matter systems where their intriguing emergent phenomena arise due to strong coupling. We will revisit the Landau paradigm of Fermi liquid theory and hence understand the properties of the non-Fermi liquid systems which cannot be described within the Landau framework, due to the destruction of the Landau quasiparticles. In particular, we will focus on critical Fermi surface states, where there is a well-defined Fermi surface, but no quasiparticles, as a result of the strong interactions between the Fermi surface and some massless boson(s). We will outline a framework to extract the low-energy physics of such systems in a controlled approximation, using the tool of dimensional regularization.