Phase diagram of the two-dimensional antiferromagnetic XY model in an external magnetic field

Antonio S. T. Pires

Roger G. Melko, Anders W. Sandvik, Douglas J. Scalapino

We present the zero-temperature phase diagram of a square lattice quantum spin-1/2 $\mathrm{XY}$ model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the $\mathrm{XY}$ order, striped or valence bond solid, staggered N\'eel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.

Michinari Monma, Tsuyoshi Horiguchi

Donald D. Betts, J. Oitmaa

Виктор Степанович Доценко, G. Uimin

A qualitative study has been performed to elucidate the critical properties of an antiferromagnetic planar system in two dimensions. Phase diagrams in the temperature-field plane differ considerably in the cases of square and triangular lattices, resulting in the latter case in coexistence of the Ising-type and vortex unbinding phase transitions.

Yizhen Huang, Gang Su

The continuous imaginary-time quantum Monte Carlo method with the worm update algorithm is applied to explore the ground-state properties of the spin-1/2 Heisenberg model with antiferromagnetic (AF) coupling J>0 and ferromagnetic (F) coupling J^{'}<0 along zigzag and armchair directions, respectively, on honeycomb lattice. It is found that by enhancing the F coupling J^{'} between zigzag AF chains, the system is smoothly crossover from one-dimensional zigzag spin chains to a two-dimensional magnetic ordered state. In absence of an external field, the system is in a stripe-ordered phase. In the presence of uniform and staggered fields, the uniform and staggered out-of-plane magnetizations appear while the stripe order remains in the xy plane, and a second-order quantum phase transition (QPT) at a critical staggered field is observed. The critical exponents of correlation length for QPTs induced by a staggered field for the cases with J>0, J^{'}<0 and J<0, J^{'}>0 are obtained to be ν=0.70046(1) and 0.7086(3), respectively, indicating that both cases belong to O(3) universality. The corresponding dynamic and susceptibility exponent z and γ/ν are fitted to be 1.006572(9), 1.9412(2) and 1.004615(8), 1.96121(9) for the two cases, respectively. The scaling behavior in a staggered field is analyzed, and the ground-state phase diagrams in the plane of coupling ratio and staggered field are presented for two cases. The temperature dependence of susceptibility and specific heat of both systems in external magnetic fields is also discussed. A Kosterlitz-Thouless phase transition is found for the present system in a uniform field.