Weakly correlated electrons on a square lattice: a renormalization group theory

TL;DR

This paper applies a one-loop renormalization group method to the weakly interacting Hubbard model on a square lattice, identifying transition temperatures and dominant correlations in different regimes, revealing antiferromagnetic and d-wave pairing behaviors.

Contribution

It introduces a renormalization group analysis to characterize phase transitions and dominant correlations in the weakly interacting Hubbard model on a square lattice.

Findings

Transition temperature T_c between metallic and ordered states is determined.

Antiferromagnetic correlations dominate in the parquet regime (T_c >> |mu|).

D-wave singlet pairing susceptibility is most divergent in the BCS regime (T_c << |mu|).

Abstract

We study the weakly interacting Hubbard model on the square lattice using a one-loop renormalization group approach. The transition temperature T_c between the metallic and (nearly) ordered states is found. In the parquet regime, (T_c >> |mu|), the dominant correlations at temperatures below T_c are antiferromagnetic while in the BCS regime (T_c << |mu|) at T_c the d-wave singlet pairing susceptibility is most divergent.