Quantum phase transitions beyond the Landau paradigm in a Sp(4) spin system

We propose quantum phase transitions beyond the Landau’s paradigm of Sp(4) spin Heisenberg models on the triangular and square lattices motivated by the exact $\text{Sp}\left(4\right)\simeq \text{SO}\left(5\right)$ symmetry of spin-3/2 fermionic cold atomic system with only $s$-wave scattering. On the triangular lattice, we study a phase transition between the $\sqrt{3}\times \sqrt{3}$ spin ordered phase and a $Z_2$ spin liquid phase; this phase transition is described by an O(8) sigma model in terms of fractionalized spinon fields, with significant anomalous scaling dimensions of spin order parameters. On the square lattice, we propose a deconfined critical point between the Neel order and the valence bond solid (VBS) order, which is described by the CP(3) model, and the monopole effect of the compact U(1) gauge field is expected to be suppressed at the critical point.

Figure 1

Mean-field solutions on triangular lattice at different $J_2/J_1$ with $J_1>0$. The $y$ axes ${\kappa }_c$ show the density of spinon condensate, which is also proportional to ${\left|z\right|}^2$ as defined in Eq. (7). ${\kappa }_c$ decreases to nearly zero (0.007) as $J_2/J_1$ decreases.

Figure 2

(Color online) (a) The SU(4) plaquette order pattern, with four SU(4) particles around the colored squares, form a SU(4) singlet. (b) The particular type of VBS state depends on the phase angle of the monopole operator.

Figure 3

(Color online) The conjectured phase diagram for the Heisenberg model in Eq. (3). By tuning one parameter $J_2/J_1$, the system evolves from the Neel state to the dimerized VBS state and the transition can be continuous. The dashed lines denote the magnitude of the Neel and VBS order parameter. $\text{SU}{\left(4\right)}_{\text{A}}$ is the SU(4) invariant point with fundamental representation on all sites and $\text{SU}{\left(4\right)}_{\text{B}}$ point is another SU(4) point with fundamental representation on one sublattice and conjugate representation on the other.