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Multidimensional Bosonization
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Bosonization of degenerate fermions yields insight both into Landau Fermi liquids, and into non-Fermi liquids. We begin our review with a pedagogical introduction to bosonization, emphasizing its applicability in spatial dimensions greater than one. After a brief historical overview, we present the essentials of the method. Well known results of Landau theory are recovered, demonstrating that this new tool of many-body theory is robust. Limits of multidimensional bosonization are tested by considering several examples of non-Fermi liquids, in particular the composite fermion theory of the half-filled Landau level. Nested Fermi surfaces present a different challenge, and these may be relevant in the cuprate superconductors. We conclude by discussing the future of multidimensional bosonization.
Forward citations
Cited by 2 Pith papers
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Critical theory of Pomeranchuk transitions via high-dimensional bosonization
The 2D Pomeranchuk transition is controlled by a Gaussian fixed point with dynamical exponent z=2 and a marginally irrelevant quartic term, not by the Hertz-Millis z=3 theory.
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Chiral Graviton Theory of Fractional Quantum Hall States
By gauging area-preserving diffeomorphisms and adding a Stueckelberg mass term, the paper constructs a nonlinear effective theory whose quadratic limit reproduces the bimetric description of the chiral spin-2 magnetoroton.
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