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

Abstract

We study the nearest-neighbor exchange (${J}_{1}$) and second-nearest-neighbor exchange (${J}_{2}$) $XY$ antiferromagnet on the honeycomb lattice using ground state series expansions around N\'eel, columnar, and dimer phases. The conventional two-sublattice $XY$ N\'eel order at small ${J}_{2}$ vanishes at ${J}_{2}/{J}_{1}=0.22\ifmmode\pm\else\textpm\fi{}0.01$ in agreement with results from density matrix renormalization group (DMRG) studies. Near the transition, we find evidence for an 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.