Quantum spin liquids (QSLs) have been the subject of great interest since Anderson’s suggestion. Recently, Kitaev proposed a canonical model of QSLs termed the Kitaev model, which provides exact realizations of QSLs with topological order and fractional excitations. Moreover, exchange interactions in some transition metal compounds with strong spin-orbit coupling may be dominated by the Kitaev-type ones. To understand magnetic properties of these compounds, the Kitaev model with additional interactions have been investigated. In this case, the Kitaev QSL is eventually replaced by some magnetically ordered phase. However, other than such scenarios of obtaining conventional magnetic orders, a possibility of nonmagnetic phases distinct from the Kiteav QSLs has yet to be well explored.

In this work, we consider the honeycomb-lattice Kitaev-Ising model and show a new liquid-like phase emerging as an intermediate phase. The ground-state phase diagram is obtained by using the exact diagonalization in finite-size clusters and the mean-field approximation in the Majorana fermion representation. We also investigate the finite-T properties using the thermal pure quantum state approach. We show that the new nonmagnetic state is well described by a spin-nematic wave-function. The liquid-liquid transition line persisting at finite T terminates at a critical point. We will show that the fractionalization of quantum spins, in particular, delocalization of Z₂ gauge fluxes plays a major role in this transition.

This work is in collaboration with Y. Kato (U Tokyo), J. Yoshitake (U Tokyo), Y. Kamiya (RIKEN), and Y. Motome (U Tokyo).

Reference:
J. Nasu, Y. Kato, J. Yoshitake, Y. Kamiya, Y. Motome: arXiv:1610.07343.