Quantum Monte-Carlo study of magnetic ordering in ZnV2O4

We study the magnetic ordering of Vanadium spinels by Quantum Monte Carlo simulations of a three-band Hubbard model. Vanadium spinels, AV$_2$O$_4$, exhibit a unique "up-up-down-down" spin ordering at low temperatures. While this magnetic ordering was originally measured in 1973, its origin has remained unclear for many years due to the lack of unbiased approaches for solving the relevant model. A three-band Hubbard model on the spinel lattice (corner sharing tetrahedra) is a minimal Hamiltonian for describing the $t_{2g}$ electrons of the V$^{2+}$ ions. One of the main difficulties is that this family of compounds belongs to the elusive intermediate-coupling regime ($U \gtrsim t$) for which there is no small parameter that can justify a perturbative expansion. We present a controlled Quantum Monte-Carlo approach to the three-band Hubbard model relevant for this materials that reproduces the up-up-down-down spin ordering. The method is free of the sign problem that is usually the main limiting factor for simulating fermionic systems in dimension higher than one.