Abstract
We study the possible ground-state configurations of two strongly coupled chains of charge neutral spin-$\frac{3}{2}$ fermionic atoms interacting via short-range van der Waals interaction. The coupling between the two chains is realized by a relatively large hopping amplitude. Exploiting the fact that such a ladder configuration can be mapped to an effective one-band model, we analyze the emerging ground states of the system. We show that various spatially inhomogeneous states, valence-bond states, and plaquette states compete depending on the filling and the ratio of the interaction strengths in the singlet and quintet scattering channel. We find that a Luttinger liquid state is the ground state of the strongly coupled ladder in an extended region of the parameter space, and we also show that a topologically nontrivial charge Haldane state can emerge in the strongly coupled ladder at quarter and three-quarter fillings.
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