Antiferromagnetic pseudogap in the two-dimensional Hubbard model deep in the renormalized classical regime

TL;DR

This paper investigates the emergence of a pseudogap in the two-dimensional Hubbard model within the renormalized classical regime, revealing how spin fluctuations influence spectral properties and gap formation at finite temperatures.

Contribution

It introduces a generalized two-particle self-consistent approach with a special algorithm to accurately describe the pseudogap regime in the 2D Hubbard model, including quantum corrections.

Findings

Pseudogap appears at higher temperatures than previously thought.

Results agree with quantum Monte Carlo benchmarks at high temperature.

Quantum corrections modify the zero-temperature antiferromagnetic gap.

Abstract

Long-wavelength spin fluctuations prohibit antiferromagnetic long-range order at finite temperature in two dimensions. Nevertheless, the correlation length starts to grow rapidly at a crossover temperature, leading to critical slowing down and to a renormalized-classical regime over a wide range of temperature, between a fraction of the mean-field transition temperature and the zero-temperature ordered state. This leads to a single-particle pseudogap of the kind observed in electron-doped cuprates. Very few theoretical methods can claim an accurate description of this regime. The challenge is that in this regime Fermi-liquid quasiparticles are already destroyed and new quasiparticles of the ordered state are not fully formed yet. Here, we study this problem for the two-dimensional Hubbard model by first generalizing the two-particle self-consistent approach. Using a special algorithm, spin fluctuations are treated in the thermodynamic limit even for large correlation lengths. The effects of Kanamori-Br\"uckner screening, of classical and of quantum fluctuations are taken into account. Results are presented at half-filling for the one-band Hubbard model with nearest-neighbor hopping. They agree well with available benchmark diagrammatic quantum Monte Carlo at high temperature where the pseudogap opens up. In addition to temperature-dependent spectral properties, we find quantum corrections to the zero-temperature renormalized mean-field antiferromagnetic gap. Finally, analytic continuation of the Matsubara results for spectral functions show that the pseudogap opens up at significantly higher temperature than was previously identified based on the Matsubara data only.