Haerter-Shastry kinetic magnetism and metallicity in the triangular Hubbard model

TL;DR

This paper investigates the effects of kinetic frustration on magnetism and metallicity in the triangular Hubbard model at finite hole density, revealing stable antiferromagnetic states, intermediate multimer phases, and persistent metallic behavior.

Contribution

It extends the understanding of kinetically frustrated magnetism in the triangular Hubbard model beyond previous work, analyzing stability and phase transitions at finite doping using DMRG.

Findings

Stable $120^{ ext{o}}$ antiferromagnetic state at finite hole density.

Existence of an intermediate multimer stripe phase.

Evidence of gapless charge excitations indicating metallicity.

Abstract

The fermionic Hubbard model, when combined with the ingredient of frustration, associated with the breaking of particle-hole symmetry, harbors a rich phase diagram. Aspects of theoretical findings associated with the nature of magnetism and metallicity, in a diverse set of parameter regimes, are now being actively investigated in triangular Hubbard cold atom and solid-state (moir\'e) based emulators. Building on the theoretical work of Haerter and Shastry [Phys. Rev. Lett. 95,087202 (2005)], we explore the impact of kinetically frustrated magnetism, a phenomenon where antiferromagnetic order emerges without any underlying magnetic interactions, at finite hole density. We numerically study the infinite-$U$ triangular Hubbard model using the density matrix renormalization group algorithm and estimate the extent of stability of the kinetically induced $120^{\circ}$ antiferromagnetic state to hole doping. Beyond the Haerter-Shastry regime, we find an intermediate phase with multimer (involving multiple correlated spins) stripes that eventually gives way to a paramagnet. We also find evidence of gapless charge excitations (metallicity) throughout the phase diagram for finite hole density. We discuss the implications at large, but finite and realistic values of $U/t$, and investigate whether kinetic magnetism and superexchange collaborate or compete.