Magnetic phase diagram of the Hubbard model with next-nearest-neighbour hopping

TL;DR

This paper maps the magnetic phases of the Hubbard model on a Bethe lattice, exploring how next-nearest-neighbour hopping influences magnetic order and density of states asymmetry.

Contribution

It introduces a detailed phase diagram considering NNN hopping effects, revealing extended ferromagnetic and antiferromagnetic regions due to DOS asymmetry.

Findings

Extended ferromagnetic regions for large |t2/t1|

Antiferromagnetic states in certain parameter regimes

DOS asymmetry influences magnetic ordering

Abstract

We calculate the magnetic phase diagram of the Hubbard model for a Bethe lattice with nearest neighbour (NN) hopping $t_1$ and next nearest neighbour (NNN) hopping $t_2$ in the limit of infinite coordination. We use the amplitude $t_2/t_1$ of the NNN hopping to tune the density of states (DOS) of the non-interacting system from a situation with particle-hole symmetry to an asymmetric one with van-Hove singularities at the lower ($t_2/t_1>0$) respectively upper ($t_2/t_1<0$) band edge for large enough $|t_2/t_1|$. For this strongly asymmetric situation we find rather extended parameter regions with ferromagnetic states and regions with antiferromagnetic states.