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

TL;DR

This paper develops an exact Wilsonian renormalization group approach for interacting fermions on a lattice, applying it to the Hubbard model to analyze superconductivity and antiferromagnetism, and deriving phase diagrams relevant to high-temperature superconductors.

Contribution

It introduces a novel RG method for lattice fermions, deriving flow equations for all vertices, and applies it to the Hubbard model to study competing orders and phase transitions.

Findings

Identifies the temperature of instability as a function of doping.

Calculates the renormalization of correlation functions for SC and AF.

Finds the dominant SC component is d-wave, and AF fluctuations are s-wave.

Abstract

We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in form of the Polchinski equation. We apply this method to the Hubbard model on a square lattice using both zero- and finite- temperature methods. Truncating the effective action at the sixth term in fermionic variables we obtain the one-loop functional renormalization equations for the effective interaction. We find the temperature of the instability Tc^{RG} as function of doping. We calculate furthermore the renormalization of the angle-resolved correlation functions for the superconductivity (SC) and for the antiferromagnetism (AF). The dominant component of the SC correlations is of the type d while the AF fluctuations are of the type s Following the strength of both SC and AF fluctuation along the instability line we obtain the phase diagram. The temperature Tc^{RG} can be identified with the crossover temperature T{co} found in the underdoped regime of the high-temperature superconductors, while in the overdoped regime Tc^{RG} corresponds to the superconducting critical temperature.