# Evolution of Nagaoka phase with kinetic energy frustrating hoppings

## TL;DR

This study uses density matrix renormalization group methods to explore how kinetic energy frustration affects the Nagaoka ferromagnetic state in the Hubbard model on different lattices, revealing a transition to antiferromagnetic order at small frustration levels.

## Contribution

It demonstrates that Nagaoka ferromagnetism persists only for small frustration and identifies the nature of the magnetic transition, highlighting the universality of classical kinetic antiferromagnetism in frustrated systems.

## Key findings

- Nagaoka ferromagnet survives up to t'/t ≈ 0.2
- Transition to antiferromagnetic order at critical t'
- Local magnetization remains classical across t'

## Abstract

We investigate, using the density matrix renormalization group, the evolution of the Nagaoka state with $t'$ hoppings that frustrate the hole kinetic energy in the $U=\infty$ Hubbard model on the anisotropic triangular lattice and the square lattice with second-nearest neighbor hoppings. We find that the Nagaoka ferromagnet survives up to a rather small $t'_c/t \sim 0.2.$ At this critical value, there is a transition to an antiferromagnetic phase, that depends on the lattice: a ${\bf Q}=(Q,0)$ spiral order, that continuously evolves with $t'$, for the triangular lattice, and the usual ${\bf Q}=(\pi,\pi)$ N\'eel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered $t'$ ($t'/t \le 1$). Our results show that the recently found classical kinetic antiferromagnetism, a perfect counterpart of Nagaoka ferromagnetism, is a generic phenomenon in these kinetically frustrated electronic systems.