Multidimensional Bosonization

TL;DR

This paper reviews multidimensional bosonization, a method that extends bosonization techniques beyond one dimension to analyze Fermi liquids and non-Fermi liquids, with applications to Landau theory, composite fermions, and cuprate superconductors.

Contribution

It provides a comprehensive pedagogical overview of multidimensional bosonization, demonstrating its robustness and exploring its limits through various non-Fermi liquid examples.

Findings

Recovering Landau Fermi liquid results using bosonization.

Applying bosonization to non-Fermi liquids like composite fermions.

Discussing challenges with nested Fermi surfaces in higher dimensions.

Abstract

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.