Competing valence-bond states of spin-$\frac{3}{2}$ fermions on a strongly coupled ladder

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.

Figure 1

The spectrum of a strongly coupled ladder for $f_l<1/2$.

Figure 2

The phase diagram of the strongly coupled ladder at $f_l=1/4$ filling. For the notation see the text.

Figure 3

Illustration of the various density-wave states at quarter filling. Blue dots at the sites and strings along the bonds denote large particle density at the site and the bond, respectively.

Figure 4

Schematic density profile of the quasiparticles in (a) the bonding and (b) antibonding states along the rungs. A similar density profile characterizes the quasiparticle density in the various density-wave-like states, namely, in (b) a site-centered or (c) a bond-centered density wave or (a) the coexistence of the two.

Figure 5

The same as in Fig. 3 for various commensurate fillings.

Figure 6

The phase diagram of the strongly coupled ladder for incommensurate fillings. Note that the value of Luttinger parameter $K_c$ depends on the filling.

Figure 7

The phase diagram of the strongly coupled ladder at $f_l=3/4$ filling. For the notation see the text.

Figure 8

The same as in Fig. 3 for $f_l=3/4$. The underlying SU(4) singlet rung quartets are also indicated with light blue strings.