Spin–orbital entanglement near quantum phase transitions

Abstract

Spin-orbital entanglement in the ground state of a one-dimensional SU(2)⊗SU(2) spin-orbital model is analyzed using exact diagonalization of finite chains. For S = 1/2 spins and T = 1/2 pseudospins one finds that the quantum entanglement is similar at the SU(4) symmetry point and in the spin-orbital valence bond state. We also show that quantum transitions in spin-orbital models turn out to be continuous under certain circumstances, in constrast to the discontinuous transitions in spin models with SU(2) symmetry. [Published in: Phys. Status Solidi (b) 244, 2378-2383 (2007 Copyright line will be provided by the publisher Rich magnetic phase diagrams of transition metal oxides and the existence of quite complex magnetic order with coexisting ferromagnetic (FM) and antiferromagnetic (AF) interactions, such as A-AF phase in LaMnO 3 or C-AF phase in LaVO 3 , originate from the intricate interplay between spin and orbital degrees of freedom -alternating orbital (AO) order supports FM interactions, whereas ferro orbital (FO) order supports AF ones [1]. While in many cases the spin and orbital dynamics are independent from each other and such classical concepts apply, the quantum fluctuations are a priori enhanced due to a potential possibility of joint spin-orbital fluctuations, particularly in the vicinity of quantum phase transitions [2]. Such fluctuations are even much stronger in t 2g than in e g systems and may dominate the magnetic and orbital correlations [3], which could then contradict the above classical expectations in certain regimes of parameters. Recently it has been realized [4] that this novel quantum behavior is accompanied by spinorbital entanglement, similar to that being currently under investigation in spin models [5].In general, any spin-orbital superexchange model derived for a transition metal compound with a perovskite lattice may be written in the following form:where γ = a, b, c labels the cubic axes -depending on the direction of a bond ij the interactions take a different form. The first term in Eq. (1) describes the superexchange interactions (J = 4t 2 /U is the superexchange constant, where t is the hopping element and U stands for the Coulomb element) between transition metal ions in the d n configuration with spin S. The orbital operatorsĴ (γ) ij andK (γ) ij depend on Hund's exchange parameter η = J H /U , which determines the excitation spectra after a virtualTherefore, realistic models of this type (some examples were given recently in Ref. [6] and analyzed using the mean field approximation in Ref. [7]) are rather involved and contain several terms). In addition, orbital interactions can also be induced by the coupling to the lattice, and appear in H orb term which depends on a second parameter V .In the limit of η = 0, however, and for t 2g orbitals,Ĵ (γ) ij andK (γ) ij operators simplify and contain only a scalar product T i · T j of T = 1/2 pseudospin operators which stand for two active t

Charge and Orbital Order in Transition Metal Oxides

“…At finite η the SU(4) degeneracy of all intersite correlations is removed -one finds T ij < C ij < S ij < 0 in the regime of spin singlet (S = 0) ground state, spin and orbital operators are entangled, and the GoodenoughKanamori rule is violated again, as it states that the spin and orbital correlations should be complementary to each other. A qualitatively similar case is found in a mathematical SU(2)⊗SU(2) model [98] (not realized in transition metal oxides), where the ground state is entangled in a broad range of parameters, including the exactly solvable case with alternating spin and orbital singlets on the bonds [99].…”

Bipartite entanglements in spin–orbital systems

“…Especially in the strongly correlated electronic systems, the orbital DOF is important for the relatively localized 3d or 4f electrons [8]. The spin-orbital entanglement has been introduced to investigate the quantum phase transition and quantum fluctuations in spin-orbital systems [9][10][11]. The bipartite entanglement property in spin-orbital coupling system is an interesting subject which deserves theoretical study.…”

Exotic Spin Order due to Orbital Fluctuations

“…Studies of such models require more sophisticated approaches than the singlesite mean field (MF) approximation or linear spin-wave expansion. Exact solutions are possible only for some one-dimensional spin-orbital models [35][36][37][38] -they also highlight the importance of quantum effects beyond simple classical approaches.…”