Functional renormalization group for extremely correlated electrons

TL;DR

This paper applies a strong-coupling functional renormalization group to the infinite-U Hubbard model, revealing significant renormalization effects, magnetic correlations, and violations of Luttinger's theorem in extreme electron correlations.

Contribution

It introduces a non-perturbative RG approach for the infinite-U limit, elucidating the low-energy physics of strongly correlated electrons with kinematic interactions.

Findings

Electronic bandwidth and quasiparticle residue decrease with density.

Formation of a polaronic continuum in the hole sector.

Violation of Luttinger's theorem in both paramagnetic and ferromagnetic regimes.

Abstract

At strong on-site repulsion $ U $, the fermionic Hubbard model realizes an extremely correlated electron system. In this regime, it is natural to derive the low-energy physics with the help of non-canonical operators acting on a projected Hilbert space without double occupancies. Using a strong-coupling functional renormalization group technique, we study the physics of such extreme correlations in the strict $ U = \infty $ limit, where only kinematic interactions due to the Hilbert space projection remain. For nearest-neighbor hopping on a square lattice, we find that the electronic spectrum is significantly renormalized, with bandwidth and quasi-particle residue strongly decreasing with increasing electron density. On the other hand, damping and particle-hole asymmetry increase, while a polaronic continuum forms in the hole sector, below the single-particle band. Fermi liquid phenomenology applies only at low densities, where the system remains paramagnetic. At higher densities, we find a bad metal with strong magnetic correlations, indicating that the ground state is the Nagaoka ferromagnet at high densities and a stripe antiferromagnet at intermediate densities. Both in the paramagnetic and the ferromagnetic regimes, we observe a violation of Luttinger's theorem.