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

TL;DR

This paper maps certain two-band models with dominant inter-band interactions onto a transverse-field $J_1$-$J_2$ Ising model in the strong-coupling limit, revealing diverse ground states and quantum critical points accessible through parameter tuning.

Contribution

It introduces three schemes to eliminate the fermionic sign problem in two-band models and demonstrates their strong-coupling behavior mapped onto an effective Ising model, expanding understanding of quantum phase transitions.

Findings

Strong-coupling ground states include quantum paramagnets and various ordered phases.

Mapping onto the transverse-field $J_1$-$J_2$ Ising model reveals quantum critical points.

Tuning band structure parameters accesses diverse phases not seen in weak-coupling regimes.

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 $J_1$-$J_2$ 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.