Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram

TL;DR

This paper explores the ground-state phase diagram of the 2D fermionic Hubbard model at moderate interactions, revealing a regime dominated by Fermi liquid physics and weak BCS instabilities, with detailed analysis of superfluid states.

Contribution

It introduces a controlled combination of diagrammatic Monte Carlo and semi-analytic methods to map the phase diagram and identify weak BCS instabilities in the model.

Findings

Weak BCS coupling constants up to U=4, n=0.6

Competition between p- and d-wave superfluid states

Controlled access to Fermi liquid regime

Abstract

A significant part of the phase diagram of the two-dimensional fermionic Hubbard model for moderate interactions and filling factors ($U < 4, \, n<0.7$) is governed by effective Fermi liquid physics with weak BCS-type instabilities. We access this regime in a controlled way by a combination of the bold-line diagrammatic Monte Carlo method with an additional ladder-diagram summation trick and semi-analytic treatment of the weak instability in the Cooper channel. We obtain the corresponding ground-state phase diagram in the $(n,U)$ plane describing the competition between the $p-$ and $d-$wave superfluid states. We also claim the values of the dimensionless BCS coupling constants controlling the superfluid $T_c$ at the phase boundaries, which prove to be very small up to $U=4, n = 0.6$.