Angular Dependence of Specific Heat and Magnetization Effects in the Kitaev Model

Abstract

We investigate the effect of a magnetic field on the Kitaev model using the equation of motion approach for the spin Green's function, considering both the case of suppressed magnetization ($m = 0$) and finite magnetization ($m \neq 0$). When magnetization is suppressed, the specific heat exhibits a clear $60^\circ$ periodicity in its angular dependence, with the locations of maxima and minima consistent with recent experimental observations in $\alpha$-RuCl$_3$. A qualitative difference in their temperature dependence is observed: the minima show gap-like behavior that may signal Majorana gap formation due to time-reversal symmetry breaking, while the maxima do not exhibit the expected gapless Majorana fermion signature. In addition, a linear-in-field effect -- distinct from magnetization -- emerges, with the characteristic temperature below which angular dependence appears increasing linearly with the magnetic field. Importantly, this directional dependence becomes quantitatively significant only at very low temperatures. When finite magnetization is included, the angular dependence of the specific heat remains, and the qualitative behavior is similar to the $m = 0$ case: the minima continue to exhibit gap-like features, while the maxima do not show signatures of gapless Majorana fermions. These results suggest that suppressing magnetization alone is insufficient to realize quantum spin liquid behavior in the Kitaev model under a magnetic field.