Exact eigenvalues and experimental signatures of Heisenberg-Kitaev interactions in spin-1/2 quantum clusters

TL;DR

This paper provides exact solutions for small spin-1/2 clusters with Heisenberg and Kitaev interactions, revealing thermodynamic signatures and phase transitions that aid in experimental detection of Kitaev physics.

Contribution

It offers analytical solutions for spin clusters with Kitaev interactions, highlighting thermodynamic signatures and phase transitions relevant for experiments.

Findings

Kitaev interactions cause a second Schottky anomaly in heat capacity.

Kitaev terms lead to nonlinear eigenvalues and quantum phase transitions.

Insights applicable to molecular magnets and extended lattices.

Abstract

We investigate the thermodynamics and energy eigenstates of a spin-1/2 coupled trimer, tetramer in a star configuration, and tetrahedron. Using a Heisenberg Hamiltonian with additional Kitaev interactions, we explore the thermodynamic signatures of the Kitaev interaction. Our results show that introducing a Kitaev interaction generates a second Schottky anomaly in the heat capacity for systems with a large K/J ratio. The Kitaev term also introduces nonlinear eigenvalues with respect to a magnetic field, pushing the clusters toward a regime similar to the incomplete Paschen-Back effect and triggering first and second-order quantum phase transitions along with robust thermodynamic behavior. Through this approach, we provide exact analytical solutions that offer insights into Kitaev interactions, both in molecular magnets and in extended systems such as honeycomb or Kagome lattices. Furthermore, we provide insight into experimental measurements for detecting Kitaev interactions in clusters.