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 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.
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We thank Andrey Chubukov, Anders Sandvik, Yoni Schattner, Jun Takahashi, and Oskar Vafek for fruitful discussions. XW acknowledges financial support from National MagLab, which is funded by the National Science Foundation, USA ( DMR-1644779 ) and the state of Florida, USA . MHC acknowledges financial support from the Villum foundation, Denmark . EB was supported by the European Research Council (ERC) under grant HQMAT (grant no. 817799 ), the US-Israel Binational Science Foundation (BSF), Israel , and the Minerva foundation, Germany . RMF is supported by the U.S. Department of Energy , Office of Science, Basic Energy Sciences, Materials Science and Engineering Division, under Award No. DE-SC0020045 . RMF also acknowledges partial support from the Research Corporation for Science Advancement, USA via the Cottrell Scholar Award.
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