Phase diagram of the frustrated quantum-XY model 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-neighbor exchange ($J_2$) XY antiferromagnet on the honeycomb lattice using ground state series expansions around N{é}el, columnar and dimer phases. The conventional two-sublattice XY N{é}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.

5 pages, 5 figures

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Cited by in corpus (2)

• Phase diagram of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ $XXZ$ model on the honeycomb lattice
• Quantum phases of the frustrated XY models on the honeycomb lattice