Deconfined Criticality in the Frustrated Heisenberg Honeycomb Antiferromagnet

Using the density matrix renormalization group, we determine the phase diagram of the spin-$1/2$ Heisenberg antiferromagnet on a honeycomb lattice with a nearest-neighbor interaction $J_1$ and a frustrating, next-nearest-neighbor exchange $J_2$. As frustration increases, the ground state exhibits Néel, plaquette, and dimer orders, with critical points at $J_2/J_1=0.22$ and 0.35. We observe that both the spin gap and the corresponding order parameters vanish continuously at both the critical points, indicating the presence of deconfined quantum criticality.

Figure 1

Phase diagram of the spin-$1/2$ Heisenberg antiferromagnet on the honeycomb lattice with a nearest-neighbor interaction $J_1$ and a frustrating, next-nearest-neighbor exchange $J_2$ as obtained from DMRG calculations.

Figure 2

Finite-size scaling of the Néel order parameter. (a) Diamond cluster with $L=3$. (b) Hexagonal cluster with $L=3$. (c),(d) Finite-size scaling of the Néel order parameter defined in Eq. (2) for diamond and hexagonal clusters. (e) Scaled Néel order parameter as a function of $\alpha =J_2/J_1$ for diamond (closed red circles) and hexagonal (open blue circles) clusters.

Figure 3

(a) Cluster geometry with $L=3$ used to establish the presence of plaquette order. (b),(c) Finite-size scaling of the spin gap and $⟨{\widehat{P}}_{\mathrm{central}}⟩$—a measure of pRVB amplitude. We find good scaling with polynomials up to cubic order in $1/L$. (d) Spin gap and $⟨{\widehat{P}}_{\mathrm{central}}⟩$ in the thermodynamic limit.

Figure 4

(a) Cluster geometry to detect dimer order. We enforce periodic boundary conditions (PBCs) along $L_y$ and open boundary conditions (OBCs) along $L_x$. (b) Finite-size scaling of $⟨\widehat{R}⟩$, with an order parameter corresponding to lattice rotational symmetry breaking. For scaling, we first take $L_x\to \infty$ and then $L_y\to \infty$. We show data points obtained by $L_x$ scaling for different fixed $L_y$ values. The points connected by the line are the final values obtained from $L_y$ scaling. (c) Finite-size scaling of the spin gap (obtained by similar finite-size scaling) as a function of $\alpha =J_2/J_1$.