Abstract
To demonstrate the role played by the von Neumann entropy (vNE) spectra in quantum phase transitions we investigate the one-dimensional anisotropic SU(2) 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 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.
Highlights
〈ij〉 ∥γ as found for the simplest systems with S = 1 2 spins: KCuF3 [1], the RTiO3 perovskites [6], LiNiO2 and NaNiO2 [7], Sr2CuO3 [8], or alkali RO2 hyperoxides [9], and for larger spins as e.g. for S = 2 in LaMnO3 [10]. In such models the parameters that determine the spin-S Heisenberg interactions stem from orbital operators Ji(jγ) and Ki(jγ)—they depend on the bond direction and are controlled by the orbital degree of freedom which is described by pseudospin operators {Ti⃗ }
These parameters are not necessarily fixed by rigid orbital order [3, 11], but quantum fluctuations of orbital occupation [12, 13] may strongly influence the form of the orbital operators, in states with spin–orbital entanglement (SOE) [14, 15]
Both III–V and II–V phase transitions arise from the SOE in the case of Ising orbital interactions
Summary
In this paper we explore a different entanglement measure, namely the vNE spectrum which monitors the vNE of ground and excited states of the system, for instance of a spin–orbital system as defined in equation (1) In this case we consider the entanglement obtained from the bipartitioning into spin and orbital degrees of freedom in the entire system [30]. Examples of strongly entangled quasi-1D t2g spin–orbital systems due to dimensional reduction are well known and we mention here just LaTiO3 [6], LaVO3 and YVO3 [13], where the latter two involve {yz, zx} orbitals along the c cubic axis; as well as px and py orbital systems in 1D fermionic optical lattices [39,40,41] This motivates us to consider the 1D spin–orbital model for S = 1 2 spins and T = 1 2 orbitals with anisotropic XXZ interaction, i.e., with reduced quantum fluctuation part in orbital interactions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
