Deformation of SU(4) singlet spin-orbital state due to Hund's rule coupling

It has been widely recognized that the interplay of spin and orbital degrees of freedom plays a crucial role in the emergence of novel magnetism in strongly correlated systems. In this context, a one-dimensional spin-orbital model with the highest SU(4) symmetry has been one of the subjects of much interests from a theoretical viewpoint, and the critical behavior of the SU(4) singlet ground state has been clarified. However, in a more realistic situation, the Hund's rule coupling should break the SU(4) symmetry. In the present work, by exploiting a density-matrix renormalization group method, we investigate a one-dimensional spin-orbital model in which the SU(4) symmetry is broken down to SU(2)$_{\rm spin}$$\times$U(1)$_{\rm orbital}$ due to the Hund's rule coupling ($J$). At $J=0$, spin and orbital correlations coincide with each other with a peak at $q=\pi/2$, indicating the SU(4) singlet state with a four-site periodicity. On the other hand, with increasing $J$, the peak position of orbital correlation changes to $q=\pi$, while that of spin correlation remains at $q=\pi/2$. We will discuss in detail how the SU(4) singlet state is deformed by the Hund's rule coupling.