Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations

This paper addresses the question of whether standard models of correlated electron systems, Hubbard and Heisenberg, show novel physics when defined on hyperbolic geometries with open boundaries. It turns out that the boundary, being extensive, plays a dominant role. At the boundary, spin fluctuations are enhanced. The metal-insulator transition observed on some geometries is a consequence of the boundary. The magnetically ordered phase at weak coupling shows macroscopic moments that cancel to form a spin-singlet ground state.