Exploring the Hubbard Model on the Square Lattice at Zero Temperature with a Bosonized Functional Renormalization Approach

TL;DR

This paper uses a functional renormalization group approach to study the phase diagram of the Hubbard model on a square lattice at zero temperature, revealing competing instabilities and phase transitions.

Contribution

It introduces a unified scheme for deriving flow equations in symmetric and symmetry broken regimes, enabling a consistent analysis of phase transitions and coexistence phenomena.

Findings

Identifies leading instabilities in d-wave superconducting and antiferromagnetic channels.

Discovers a first order transition between commensurate and incommensurate antiferromagnetism.

Shows coexistence and mutual exclusion of superconductivity and antiferromagnetism at different scales.

Abstract

We employ the functional renormalization group to investigate the phase diagram of the $t-t'$ Hubbard model on the square lattice with finite chemical potential $\mu$ at zero temperature. A unified scheme to derive flow equations in the symmetric and symmetry broken regimes allows a consistent continuation of the renormalization flow in the symmetry broken regimes. At the transition from the symmetric regime to the symmetry broken regimes, our calculation reveals leading instabilities in the d-wave superconducting and antiferromagnetic channels. Furthermore, we find a first order transition between commensurate and incommensurate antiferromagnetism. In the symmetry broken regimes our flow equations are able to renormalize around a changing Fermi surface geometry. We find a coexistence of d-wave superconductivity and antiferromagnetism at intermediate momentum scales k. However, there is a mutual tendency of superconductivity and antiferromagnetism to repel each other at even smaller scales k, which leads to the eradication of the coexistence phase in the limit of macroscopic scales.