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arXiv · 1207.5304

Gauge theory of topological phases of matter

Juerg Froehlich·Philipp Werner
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Abstract

We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our analysis leads to a "gauge theory of states of matter" complementary to the well known Landau theory of order parameters. We illustrate the power of our approach by deriving and interpreting the gauge-invariant effective actions of (topological) superconductors, 2D electron gases exhibiting the quantized Hall- and spin-Hall effect, 3D topological insulators, as well as axion electrodynamics. We also use the theory to elucidate the structure of surface modes in these systems.

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Juerg Froehlich, Philipp Werner. 2013-03-06. Gauge theory of topological phases of matter. https://doi.org/10.1209/0295-5075%2F101%2F47007

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