Phase diagram of a one-dimensional spin-orbital model

Itoi, Chigak; Qin, Shaojin; Affleck, Ian

doi:10.1103/physrevb.61.6747

Cited by 108 publications

(167 citation statements)

References 21 publications

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“…This model can be thought of as a 2D generalization of the wellstudied [45][46][47][48][49] 1D spin-orbital model. We first discuss the classical limit of this model.…”

Section: B the Kx-modelmentioning

confidence: 99%

Quantum magnetism on the Cairo pentagonal lattice

2012

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We present an extensive analytical and numerical study of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, the dual of the Shastry-Sutherland lattice with a close realization in the S = 5/2 compound Bi2Fe4O9. We consider a model with two exchange couplings suggested by the symmetry of the lattice, and investigate the nature of the ground state as a function of their ratio x and the spin S. After establishing the classical phase diagram we switch on quantum mechanics in a gradual way that highlights the different role of quantum fluctuations on the two inequivalent sites of the lattice. The most important findings for S = 1/2 include: (i) a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism at small x (related to an emergent J1-J2 effective model with J2 ≫ J1), and (ii) a non-magnetic and possibly spin-nematic phase with d-wave symmetry at intermediate x.

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“…This model can be thought of as a 2D generalization of the wellstudied [45][46][47][48][49] 1D spin-orbital model. We first discuss the classical limit of this model.…”

Section: B the Kx-modelmentioning

confidence: 99%

Quantum magnetism on the Cairo pentagonal lattice

2012

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“…Its phase diagram in the (x, y) plane consists of five distinct phases which result from the competition between effective AF and FM spin (AO and FO pseudospin) interactions on the bonds [8]. First of all, the spin and pseudospin correlations are FM-FO, S ij = T ij = 1 4 , if x < − 1 4 and y < − 1 4 .…”

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Spin–orbital entanglement near quantum phase transitions

Oleś

Horsch

Khaliullin

2007

Physica Status Solidi (b)

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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

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“…The application of an exterior field will make each energy level corresponding to a multiplet that carries out a SU(4) irreducible representation split into Zeemann sublevels. If g t = 0.0, the energy level of an SU (4) 4 ] with m 1 = m 2 and m 3 = m 4 , i.e., M ′ = 2M ′′ , N + M ′ = 2M . This implies that the evo-lution of Young tableau caused by the exterior field is realized by moving a couple of boxes lying in the third and the fourth row to the first and the second row.…”

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“…Kz,75.10.Jm, Recently, much attention has been focused on strongly correlated electrons with orbital degrees of freedom [1,2,3,4,5,6,7] due to progress in experimental studies of transition metal and rare earth compounds such as LaMnO 3 , CeB 6 and TmTe. Examples of spin-orbital systems in one dimension include quasi-one-dimensional tetrahis-dimethylamino-ethylene(TDAE)-C 60 [8], artificial quantum dot arrays [9] and degenerate chains in Na 2 Ti 2 Sb 2 O and Na 2 V 2 O 5 compounds [10,11,12].…”

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confidence: 99%

Magnetic properties of an SU(4) spin-orbital chain

2002

Phys. Rev. B

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In this paper, we study the magnetic properties of the one-dimensional SU(4) spin-orbital model by solving its Bethe ansatz solution numerically. It is found that the magnetic properties of the system for the case of gt = 1.0 differs from that for the case of gt = 0.0. The magnetization curve and susceptibility are obtained for a system of 200 sites. For 0 < gt < gs, the phase diagram depending on the magnetic field and the ratio of Landé factors, gt/gs, is obtained. Four phases with distinct magnetic properties are found.PACS number:75.30. Kz,75.10.Jm, Recently, much attention has been focused on strongly correlated electrons with orbital degrees of freedom [1,2,3,4,5,6,7] due to progress in experimental studies of transition metal and rare earth compounds such as LaMnO 3 , CeB 6 and TmTe. Examples of spin-orbital systems in one dimension include quasi-one-dimensional tetrahis-dimethylamino-ethylene(TDAE)-C 60 [8], artificial quantum dot arrays [9] and degenerate chains in Na 2 Ti 2 Sb 2 O and Na 2 V 2 O 5 compounds [10,11,12]. In these systems, the low-lying electron states have orbital degeneracy in addition to the spin degeneracy. This may result in various interesting properties associated with the orbital degrees of freedom in Mott insulating phases. For example, the magnetic ordering is influenced by the orbital structure which may change with pressure, or the magnetization is a nonlinear function of magnetic field even in the case of an isotropic exchange interaction ofThe spin model with orbital degeneracy in a magnetic field was studied by means of effective field theories [5] recently. It has been shown that there exists critical behavior under magnetic field. For a nonperturbative understanding of the magnetic properties of the model, the Bethe-ansatz solution of the SU(4) model is applicable when the exterior magnetic field is applied since the total z component of spin and orbital is a good quantum number. Although Ref.[6] studied the magnetic properties in terms of the Bethe-ansatz method, their result involves only a special case because the Landé factor was not taken into account. In present paper, we study the model in the presence of an exterior field by solving the Bethe-ansatz equation numerically meanwhile taking account of the Landé g factor. We obtain a rich phase diagram in comparison to what was obtained in [6]. Our results shed new light on the understanding of more realistic systems. The quantum phase transition(QPT) [14] concluded from such a system is speculated to be found in experiments.The one-dimensional quantum spin 1/2 system with twofold orbital degeneracy is modelled by [15,16] where the coupling constant is set to unity. The Hamiltonian (1) has not only SU(2)×SU(2) symmetry, but also an enlarged SU(4) symmetry [16]. It was solved by the Bethe-ansatz approach, the obtained secular equation reads [17,18]:where θ ρ (x) = −2 tan −1 (x/ρ). The quantum numbers {I a , J a , K a } specify a state in which there are N − M number of sites in the state • {I a , J a , K a } are consecu...

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Phase diagram of a one-dimensional spin-orbital model

Cited by 108 publications

References 21 publications

Quantum magnetism on the Cairo pentagonal lattice

Quantum magnetism on the Cairo pentagonal lattice

Spin–orbital entanglement near quantum phase transitions

Magnetic properties of an SU(4) spin-orbital chain

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