Spin Seebeck effect in the Kitaev spin liquid*

Quantum spin liquids (QSLs) have nontrivial elementary excitations due to quantum entanglement. However, these elementary excitations are not easy to detect, and this is one of the reasons why the identification of QSLs is difficult. In one-dimensional QSLs, the spinon-mediated spin Seebeck effect (SSE) has been discovered [1], indicating that the SSE is useful for characterizing QSLs. However, the SSE for QSLs in more than one dimension remains unexplored both theoretically and experimentally. In this study, we focus on two-dimensional Kitaev QSLs and analyze the SSE based on the tunnel spin-current theory using the density matrix renormalization group method and the time-dependent variational principle that accurately incorporate quantum many-body effects. In addition, we examine the low-field and the high-field behaviors by the perturbation theory and the spin-wave theory, respectively. As a result, we found that the SSE changes its sign depending on the sign of the Kitaev interaction. This indicates that the lowest energy excitation in the Kitaev QSL, the Majorana fermions, contribute to the spin current with (up-)down-spin like nature when the Kitaev interaction is (anti-)ferromagnetic. Our results suggest that the Majorana fermions excitations contribute not only to the heat flow but also to the thermal spin current transport, and that their signatures are useful for detecting QSLs.

[1] D. Hirobe et al., Nat. Phys. 13, 30 (2017).