Quantum phase transition in the four-spin exchange antiferromagnet

We study the $S=1/2$ Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to Néel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.

Figure 1

(Color online) Dimer pattern in the quantum-disordered (VBS) phase, $K/J>{\left(K/J\right)}_c$.

Figure 2

(Color online) Triplon excitation gap $\Delta =\omega \left({\mathbf{k}}_{\text{AF}}\right)$ in various approximations. The point $\Delta \to 0$ corresponds to transition to the Néel phase.

Figure 3

(Color online) Renormalization of quantum fluctuations by resummation of a ladder series with Eq. (13) at the vertices.

Figure 4

(Color online) (a) Singlet bound-state energy $E_s$ (black), binding energy $ϵ=2\Delta -E_s$ (blue), and the triplon gap $\Delta$ (red). (b) Triplon density $n_t$. (c) Dimer order parameters. Dashed parts of the lines represent points corresponding to rapid growth of the quasiparticle density.