Partial continuum limit of the 2D Hubbard model

TL;DR

This paper develops a partial continuum limit of the 2D Hubbard model, deriving an effective quantum field theory that reveals spin-charge separation and connects to a 2D Wess-Zumino-Witten model.

Contribution

It introduces a novel partial continuum limit for the 2D Hubbard model and derives an effective field theory with bosonization and solvable interacting fermion models.

Findings

Bosonization of nodal fermions leads to spin-charge separation.

Identification of an exactly solvable model of interacting 2D fermions.

Proposals for treating antinodal fermions in the effective theory.

Abstract

An effective quantum field theory of the 2D Hubbard model on a square lattice near half-filling is presented and studied. This effective model describes so-called nodal and antinodal fermions, and it is derived from the lattice model using a certain partial continuum limit. It is shown that the nodal fermions can be bosonized, which leads to spin-charge separation and a 2D analogue of a Wess-Zumino-Witten model. A bosonization formula for the nodal fermion field operator is obtained, and an exactly solvable model of interacting 2D fermions is identified. Different ways of treating the antinodal fermions are also proposed.