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

Xiaoyu Wang, Morten H. Christensen, Erez Berg, Rafael M. Fernandes

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Article number168522
JournalAnnals of Physics
StatePublished - Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.


Dive into the research topics of 'Strong-coupling expansion of multi-band interacting models: Mapping onto the transverse-field J1-J2 Ising model'. Together they form a unique fingerprint.

Cite this