Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control

TL;DR

This paper explores how kinetic frustration in a Hubbard model causes a quantum phase transition from Nagaoka ferromagnetism to spiral spin-density waves, with implications for cold-atom and moiré systems.

Contribution

It demonstrates the instability of Nagaoka ferromagnetism due to kinetic frustration and characterizes the resulting quantum phase transition using analytic, numerical, and variational methods.

Findings

Critical frustration induces a transition from ferromagnetism to spiral spin-density wave.

The transition persists at low finite hole densities, relevant for experimental platforms.

A variational approach explains the magnon band deformation mechanism.

Abstract

We investigate the Nagaoka-Thouless (NT) ferromagnetic instability in the strongly interacting $t$-$t'$ Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin-polaron when the kinetic frustration $t'/t$ exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group simulations reveal a quantum phase transition from the NT ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moir\'e Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite density via frustration-induced magnon band deformation.