Spin-orbital Chain Research Articles

Fractionalization, entanglement, and separation: Understanding the collective excitations in a spin-orbital chain

Using a combined analytical and numerical approach, we study the collective spin and orbital excitations in a spin-orbital chain under a crystal field. Irrespective of the crystal field strength, these excitations can be universally described by fractionalized fermions. The fractionalization phenomenon persists and contrasts strikingly with the case of a spin chain, where fractionalized spinons cannot be individually observed but confined to form magnons in a strong magnetic field. In the spin-orbital chain, each of the fractional quasiparticles carries both spin and orbital quantum numbers, and the two variables are always entangled in the collective excitations. Our result further shows that the recently reported separation phenomenon occurs when crystal fields fully polarize the orbital degrees of freedom. In this case, however, the spinon and orbiton dynamics are decoupled solely because of a redefinition of the spin and orbital quantum numbers.

Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory

Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation [Phys. Rev. B 91, 165102 (2015)], we apply the same formalism to the case of a spin chain in the external magnetic field. It occurs that in this case, which corresponds to N=2 in the approximation, the large-N mean-field theory cannot qualitatively reproduce the spin excitation spectra at high magnetic fields, which polarize more than 50% of the spins in the magnetic ground state. This, rather counterintuitively, shows that the physics of a spin chain can under some circumstances be regarded as more complex than the physics of a spin-orbital chain.

Erratum: Quantum phase transitions in a strongly entangled spin-orbital chain: A field-theoretical approach [Phys. Rev. B83, 205132 (2011)

Erratum: Quantum phase transitions in a strongly entangled spin-orbital chain: A field-theoretical approach [Phys. Rev. B<b>83</b>, 205132 (2011)

Quantum phase transitions in a strongly entangled spin-orbital chain: A field-theoretical approach

Motivated by recent experiments on quasi-one-dimensional vanadium oxides, we study quantum phase transitions in a one-dimensional spin-orbital model describing a Haldane chain and a classical Ising chain locally coupled by the relativistic spin-orbit interaction. By employing a field-theoretical approach, we analyze the topology of the ground-state phase diagram and identify the nature of the phase transitions. In the strong coupling limit, a long-range N\'eel order of entangled spin and orbital angular momenta appears in the ground state. We find that, depending on the relative scales of the spin and orbital gaps, the linear chain follows two distinct routes to reach the N\'eel state. First, when the orbital exchange is the dominating energy scale, a two-stage ordering takes place in which the magnetic transition is followed by melting of the orbital Ising order; both transitions belong to the two-dimensional Ising universality class. In the opposite limit, the low-energy orbital modes undergo a continuous reordering transition which represents a line of Gaussian critical points. On this line the orbital degrees of freedom form a Tomonaga--Luttinger liquid. We argue that the emergence of the Gaussian criticality results from merging of the two Ising transitions in the strong hybridization region where the characteristic spin and orbital energy scales become comparable. Finally, we show that, due to the spin-orbit coupling, an external magnetic field acting on the spins can induce an orbital Ising transition.

Model for frustrated spin-orbital chains as applied toCaV2O4

Motivated by recent interest in quasi-one-dimensional compound ${\text{CaV}}_{2}{\text{O}}_{4}$, we study the ground states of a spin-orbital chain characterized by an Ising-like orbital Hamiltonian and frustrated interactions between $S=1$ spins. The on-site spin-orbit interaction and the Jahn-Teller effect compete with intersite superexchange leading to a rich phase diagram in which an antiferro-orbital phase is separated from the orbital paramagnet by a continuous Ising transition. Two distinct spin liquids depending on the underlying orbital order are found in the limit of small spin-orbit coupling. In the opposite limit, the zigzag chain behaves as a spin-2 chain with Ising anisotropy. The implications for ${\text{CaV}}_{2}{\text{O}}_{4}$ are discussed.

Spin-orbital entanglement and quantum phase transitions in a spin-orbital chain withSU(2)×SU(2)symmetry

Spin-orbital entanglement in quantum spin-orbital systems is quantified by a reduced von Neumann entropy, and is calculated for the ground state of a coupled spin-orbital chain with $SU(2)\times SU(2)$ symmetry. By analyzing the discontinuity and local extreme of the reduced entropy as functions of the model parameters, we deduce a rich phase diagram to describe the quantum phase transitions in the model. Our approach provides an efficient and powerful method to identify phase boundaries in a system with complex correlation between multiply degrees of freedom.

R-matrices for integrable SU(2) × U(1)-symmetric spin-orbital chains

The Yang–Baxter equation for an SU(2) × U(1)-symmetric spin-orbital chain was solved using the special computer algorithm developed by the author. The seven new R-matrices separated into four groups are presented. Among the obtained integrable models there are special cases related to 1D ferromagnet TDAE-C60, 1D superconductors AC60 (A = K, Cs, Rb), the quarter-filled ladder compound NaV2O5 and the model of correlated electrons on a chain of Berry phase molecules.

Onset of metallic ferromagnetism in a doped spin–orbital chain

AbstractStarting from a spin–orbital model for doped manganites, we investigate a competition between ferromagnetic and antiferromagnetic order in a one‐dimensional model at finite temperature. The magnetic and orbital order at half filling support each other and depend on a small antiferromagnetic superexchange between t2g spins and on an alternating Jahn–Teller potential. The crossover to a metallic ferromagnetic phase found at finite doping is partly suppressed by the Jahn–Teller potential which may localize eg electrons. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Phase diagram and symmetry breaking of an SU(4) spin-orbital chain in a generalized external field

The ground state phases of a one-dimensional SU(4) spin-orbital Hamiltonian in a generalized external field are studied on the basis of Bethe-ansatz solution. Introducing three Land\'e $g$ factors for spin, orbital and their products in the SU(4) Zeeman term, we discuss systematically the various symmetry breaking. The magnetization versus external field are obtained by solving Bethe-ansatz equations numerically. The phase diagrams corresponding to distinct residual symmetries are given by means of both numerical and analytical methods.

Magnetization plateau and quantum phase transitions in a spin-orbital model

A spin-orbital chain with different Landé g factors and one-ion anisotropy is studied in the context of the thermodynamical Bethe ansatz. It is found that there exists a magnetization plateau resulting from the different Landé g factors. Detailed phase diagram in the presence of an external magnetic field is presented both numerically and analytically. For some values of the anisotropy, the four-component system undergoes five consecutive quantum phase transitions when the magnetic field varies. We also study the magnetization in various cases, especially its behaviors in the vicinity of the critical points. For the SU(4) spin-orbital model, explicit analytical expressions for the critical fields are derived, with excellent accuracy compared with numerics.

Excitations and Dynamics of Spin-Orbital Chains

The low-energy excitations and dynamics of a spin-orbital chain are calculated within a variational framework based on dimer states, exact diagonalization and the dynamical Density Matrix Renormalization Group (DMRG). In its dimerized phase, the spin-orbital chain exhibits a rich interplay of solitonic and magnonic excitations. While a solitonic excitation is the lowest excitation in a narrow region around the exactly solvable dimer point, magnonic excitations govern the phase transitions to neighbouring phases. Numerical calculations confirm that the curvature of the magnonic excitations is exactly flat on the so-called dimer line, changing sign across the line. This statement is not true for the solitonic excitations, which determine the lower edge of the excitation spectrum in the vicinity of the dimer line. DMRG calculations suggest that low-lying solitonic excitations may be experimentally hard to observe, with most spectral weight in higher-lying magnons.

Dynamical properties of spin-orbital chains in a magnetic field

The excitation spectrum of the one-dimensional spin-orbital model in a magnetic field is studied, using a recently developed dynamical density matrix renormalization group technique. The method is employed on chains with up to 80 sites, and examined for test cases such as the spin-1/2 antiferromagnetic Heisenberg chain, where the excitation spectrum is known exactly from the Bethe Ansatz. In the spin-orbital chain, the characteristic dynamical response depends strongly on the model parameters and the applied magnetic field. The coupling between the spin and orbital degrees of freedom is found to influence the incommensuration at finite magnetizations. In the regions of the phase diagram with only massive spin and orbital excitations, a finite field is required to overcome the spin gap. An incommensurate orbital mode is found to become massless in this partially spin-polarized regime, indicating a strong coupling between the two degrees of freedom. In the critical region with three elementary gapless excitations, a prominent particle-hole excitation is observed at higher energies, promoted by the biquadratic term in the model Hamiltonian of the spin-orbital chain.