Strong coupling phases of the $t-t'$ Hubbard model

TL;DR

This paper investigates the phase diagram of the strong coupling $t-t'$ Hubbard model near van Hove singularities using exact diagonalization, revealing competing ferromagnetic and $d$-wave condensate phases.

Contribution

It provides a detailed analysis of the phase competition in the $t-t'$ Hubbard model at strong coupling, highlighting the coexistence of ferromagnetic and $d$-wave-like phases.

Findings

Identification of ferromagnetic tendencies in certain parameter regimes.

Evidence for a $d$-wave condensate competing with ferromagnetism.

Phase diagram mapping near van Hove singularities.

Abstract

We study the strong coupling regime of the $t-t'$ Hubbard model,filled up to the level of the van Hove singularities, by means of an exact diagonalization approach. We characterize the different phases of the model by the different sectors of the Hilbert space with given quantum numbers. By looking for the ground state of the system, we find essentially the competition between a state with incipient ferromagnetism and other mimicking a $d$-wave condensate, which has the lowest energy in a large region of the phase space.