Exact diagonalization studies of an effective model for quantum kagome ice

We study the spin-1/2 kagome Heisenberg XYZh model in the so-called quantum kagome ice regime[1]. From our recent topological entanglement entropy and thermal entropy studies, we find that the system does not show a Z₂ topological order down to β=48, while the thermal entropy down to β=200 is consistent with the residual entropy of a classical kagome ice in a magnetic field [2]. Using degenerate perturbation theory (DPT) out of the classical ice manifold, we derive an effective model which shows an intricate competition between the ring-exchange and diagonal processes. Here, we perform exact diagonalization on the effective Hamiltonian. By tuning the weight of the diagonal term, we find that the competition can lead to a quasi-degenerate energy spectrum, consistent with the Quantum Monte Carlo simulation results.

[1] J. Carrasquilla, Z. Hao and R. G. Melko, Nature communications 6 (2015)
[2] K.-H. Wu, Y.-P. Huang and Y.-J. Kao arXiv:1806.08145