Single-band Triangular Lattice Hubbard Model with Tunable Anisotropy from Twisted Diamond Homobilayers

Abstract

The ground-state properties of the single-band triangular lattice Hubbard model with hopping anisotropy and strong interactions remain elusive so far. Here we show that twisted diamond homobilayers with band extrema at $Y$ valley can realize weakly-coupled chains with quasi-1D band structure; applying displacement field generates interchain hopping, transforming this quasi-1D system into a 2D one. The low-energy physics can be described by localized Wannier functions on the triangular lattice with tunable hopping anisotropy, providing a promising platform for studying the anisotropic triangular lattice Hubbard model. We further employ density matrix renormalization group to study this model with interaction $U=10t$ and anisotropy $0.5\leq t'/t\leq 1.5$ at half filling, and obtain a rich ground state phase diagram, including a chiral spin liquid phase, non-magnetic phases, and a N\'eel antiferromagnetic phase. This work provides a first realization of displacement-field tuned anisotropy in a single-band triangular Hubbard model within moir\'e systems, establishing them as a promising platform to investigate intriguing correlated physics with tunable anisotropy.