Mott-Insulator Phases of Spin-$3/2$ Fermions in the Presence of Quadratic Zeeman Coupling

We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-$3/2$ fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an $\mathrm{SU}(2)\otimes \mathrm{SU}(2)$ symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-$1/2$ Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Néel order in spin-$1/2$ gases.

Figure 1

Phase diagram for spin-$3/2$ fermions as a function of the relative coupling constant $g$ and the QZE $q$. We depict the chirality $\tau$ (density plot), the singlet-triplet crossing in the excitation spectrum (squares), the jump of the critical exponent $\gamma$ to $-1$ (circles), the critical $q_{\mathrm{cr}}$ expected from two-band theory (triangle), and the $J_2/J=0.25$ line resulting from a strong-coupling analysis (white curve). See text.

Figure 2

(a) Chirality $\tau$ and (c) critical exponent $\gamma$ as a function of $q$, for different values of $g$. Panel (b) shows $\tau$ at the field-induced PTs in Fig. 1. DMRG results with 36 sites.