Exact eigenstates and thermodynamic signatures of Kitaev interactions in a quantum three-sided star tetramer*

We investigate the thermodynamics and energy eigenstates of a spin-1/2 tetramer in a three-sided star configuration. Using a Heisenberg Hamiltonian with additional Kitaev interactions, we examine the thermodynamic signature of the Kitaev interaction for this tetramer. We find that the addition of a Kitaev interaction will produce a secondary peak in heat capacity for systems with a large K/J ratio and additional shifts in the energy eigenstates. These effects become enhanced with the application of a magnetic field, which is consistent with theoretical and experimental realizations for long-range order systems. Therefore, by examining a cluster in this manner, we can produce exact analytical solutions that can shed light on Kitaev interactions in more extensive systems like the honeycomb or Kagome lattices.