Strong-coupling expansion of multi-band interacting models: Mapping onto the transverse-field J1-J2 Ising model

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 signproblem-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 J(1)-J(2) 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 weak-coupling 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. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study investigates a class of two-dimensional two-band microscopic models with dominant inter-band repulsive interactions, proposing constrained schemes to overcome the fermionic sign-problem for efficient Quantum Monte Carlo simulations. The behavior of the models in the strong-coupling regime is studied, revealing a variety of ground states and quantum critical points accessible by varying the band structure parameters. The comparison with the single-band Hubbard model shows differences in strong-coupling behavior.