Strong-coupling expansion of multi-band interacting models: mapping onto the transverse-field $J_1$-$J_2$ Ising model

Abstract

We investigate a class of two-dimensional two-band microscopic models in which the inter-band repulsive interactions play the dominant role. We first demonstrate three different schemes of constraining the ratios between the three types of inter-band interactions -density-density, spin exchange, and pair-hopping -that render the model free of the fermionic sign-problem for any filling and, consequently, amenable to efficient Quantum Monte Carlo simulations. We then study the behavior of these sign-problem-free models in the strong-coupling regime. In the cases where spin-rotational invariance is preserved or lowered to a planar symmetry, the strong-coupling ground state is a quantum paramagnet. However, in the case where there is only a residual Ising symmetry, the strong-coupling expansion maps onto the transverse-field J1-J2 Ising model, whose pseudospins are associated with local inter-band magnetic order. We show that by varying the band structure parameters within a reasonable range of values, a variety of ground states and quantum critical points can be accessed in the strong-coupling regime, some of which are not realized in the weakcoupling regime. We compare these results with the case of the single-band Hubbard model, where only intra-band repulsion is present, and whose strong-coupling behavior is captured by a simple Heisenberg model.

Reentrance of the Disordered Phase in the Antiferromagnetic Ising Model on a Square Lattice with Longitudinal and Transverse Magnetic Fields

“…Besides, atoms in Rydberg states are governed by the van der Waals interaction. It will also be a subject of future study to investigate the Ising model with more realistic long-range interaction [40] and related models in geometrically frustrated lattices [41][42][43].…”