Entanglement driven phase transitions in spin–orbital models

To demonstrate the role played by the von Neumann entropy (vNE) spectra in quantum phase transitions we investigate the one-dimensional anisotropic SU(2)$\otimes XXZ$ spin–orbital model with negative exchange parameter. In the case of classical Ising orbital interactions we discover an unexpected novel phase with Majumdar–Ghosh-like spin–singlet dimer correlations triggered by spin–orbital entanglement (SOE) and having $k=\pi /2$ orbital correlations, while all the other phases are disentangled. For anisotropic XXZ orbital interactions both SOE and spin–dimer correlations extend to the antiferro-spin/alternating-orbital phase. This quantum phase provides a unique example of two coupled order parameters which change the character of the phase transition from first-order to continuous. Hereby we have established the vNE spectral function as a valuable tool to identify the change of ground state degeneracies and of the SOE of elementary excitations in quantum phase transitions. (paper)