Exact bosonization in two spatial dimensions and a new class of lattice gauge theories

TL;DR

This paper introduces a 2d bosonization method that maps fermionic systems to lattice gauge theories, preserving locality and establishing an equivalence in simply-connected spaces, with applications to various models including the Hubbard model.

Contribution

It presents a novel 2d bosonization technique that extends the Jordan-Wigner transformation, providing a new way to analyze fermionic systems via lattice gauge theories.

Findings

The bosonization map is an equivalence for simply-connected spaces.

Examples include free fermions on square and honeycomb lattices.

The corresponding gauge theories contain Chern-Simons-like terms.

Abstract

We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization map is an equivalence. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model. We describe Euclidean actions for the corresponding lattice gauge theories and find that they contains Chern-Simons-like terms. Finally, we write down a fermionic dual of the gauged Ising model (the Fradkin-Shenker model).