Abstract
Square lattice Hubbard models with tunable hopping ratio t'/t are highly promising for realizing a variety of quantum phases and for shedding light on key puzzles in correlated quantum materials, including higher-temperature superconductivity. We show that twisted square lattice homo-bilayers generically offer such tunability when the flat bands originate from the corner of the Brillouin zone. We reveal an emergent symmetry at low twist-angles, absent in single layers, that necessitates the vanishing of nearest neighbor hopping (t=0). This symmetry can be lifted by an inter-layer displacement field or by an in-plane magnetic field, introducing tunable t and anisotropy, allowing access to a wide range of t'/t ratios for correlated electrons on a moir\'e square lattice.