Phase diagram of the frustrated quantum-XY model on the honeycomb lattice studied by series expansions: Evidence for proximity to a bicritical point

We study the nearest-neighbor exchange ($J_1$) and second-neighbor exchange ($J_2$) XY antiferromagnet on the honeycomb lattice using ground state series expansions around N{\'e}el, columnar and dimer phases. The conventional two-sublattice XY N{\'e}el order at small $J_2$ vanishes at $J_2/J_1=0.22\pm 0.01$ in agreement with results from Density Matrix Renormalization Group (DMRG) studies. Near the transition, we find evidence for an {\it approximate} emergent symmetry between XY and Ising degrees of freedom, namely the nearest-neighbor Ising and XY spin correlations become nearly equal. This suggests that the system is close to a bicritical point separating XY and Ising orders. At still larger $J_2/J_1$ the columnar and dimer energies are found to be nearly degenerate. At even larger $J_2$ the columnar phase is obtained. The ground state energies in all three phases are in good agreement with the values found in the DMRG studies.