Signatures of the Transition between Topologically and Magnetically Ordered Ground States in the Schwinger-Boson Mean Field Theory of Frustrated Quantum Antiferromagnets - An analysis of the triangular lattice Heisenberg model with nearest and next nearest neighbour interactions

Abstract

We present three different methods of finding the critical spin value $S_c$ of the quantum phase transition between the spin liquid and the Néel order phase on the mean field triangular Heisenberg antiferromagnet at $T=0$K. These methods are: using the sublattice magnetization as an order parameter, looking at the scaling of the energy difference of topologically degenerate states in different phases, and the quantum fidelity approach. All of these methods are able to pick up the signal of the phase transition, and their estimated numerical values of $S_c$ agree for systems where the relative strength of next nearest neighbour interaction compared to the nearest neighbour interaction is small. For the relative interaction strength $j=0$ and $j=0.1$, all three methods predict $S_c\approx0.21$ and $S_c\approx0.25$ respectively, while $j=0.2$ gives deviating results. This deviation might be caused by the influence of other magnetically ordered states that we have not accounted for in our calculations, and so we restrict the validity of our results to $j<0.125$.