Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model

TL;DR

This paper uses a dynamical functional renormalization group approach combined with mean-field theory to analyze antiferromagnetism and pairing in the 2D Hubbard model, revealing a superconducting dome around 15% doping.

Contribution

It introduces a full frequency-dependent FRG method to study order parameters and critical temperatures, confirming previous static results and providing detailed phase diagram insights.

Findings

Robust pairing coexists with antiferromagnetism over a wide doping range.

Critical temperature aligns with pseudogap crossover temperature.

Superconducting dome centered at 15% hole doping in the phase diagram.

Abstract

We analyze the interplay of antiferromagnetism and pairing in the two dimensional Hubbard model with a moderate repulsive interaction. Coupled charge, magnetic and pairing fluctuations above the energy scale of spontaneous symmetry breaking are treated by a functional renormalization group flow, while the formation of gaps and order below that scale is treated in mean-field theory. The full frequency dependences of interaction vertices and gap functions is taken into account. We compute the magnetic and pairing gap functions as a function of doping $p$ and compare with results from a static approximation. In spite of strong frequency dependences of the effective interactions and of the pairing gap, important physical results from previous static functional renormalization group calculations are confirmed. In particular, there is a sizable doping regime with robust pairing coexisting with N\'eel or incommensurate antiferromagnetism. The critical temperature for magnetic order is interpreted as pseudogap crossover temperature. Computing the Kosterlitz-Thouless temperature from the superfluid phase stiffness, we obtain a superconducting dome in the $(p,T)$ phase diagram centered around 15 percent hole doping.