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Physical review. B, Condensed matter

Correlated spin and orbital dimerizations in spin-orbital models

Swapan Kumar Pati, Rajiv R. P. Singh

Published Mar 1, 2000• 14 citations
Publisher

Abstract

We study a one-dimensional spin-orbital model with Heisenberg symmetry for spins and $\mathrm{XY}$ symmetry for orbital degrees of freedom. We establish the ground-state phase diagram of this model. The gapless phases of the model consist of fully polarized ferromagnetic spin states together with the filled Jordan-Wigner Fermi sea for the orbitals. Two such phases, with ferromagnetic and antiferromagnetic $\mathrm{XY}$ correlations for the orbitals, are found. All other phases are found to have a spin gap with degenerate ground states. Two types of correlated spin and orbital dimerizations are observed: (i) spin singlet with orbital singlet in alternating rungs and (ii) spin singlet with orbital triplet in the same rung. The phase boundaries, energy gaps, and order parameters are evaluated using the density matrix renormalization group method.

DOI
10.1103/physrevb.61.5868

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We study a one-dimensional spin-orbital model with Heisenberg symmetry for spins and XY\mathrm{XY}XY symmetry for orbital degrees of freedom. We establish the ground-state phase diagram of this model. The gapless phases of the model consist of fully polarized ferromagnetic spin states together with the filled Jordan-Wigner Fermi sea for the orbitals. Two such phases, with ferromagnetic and antiferromagnetic XY\mathrm{XY}XY correlations for the orbitals, are found. All other phases are found to have a spin gap with degenerate ground states. Two types of correlated spin and orbital dimerizations are observed: (i) spin singlet with orbital singlet in alternating rungs and (ii) spin singlet with orbital triplet in the same rung. The phase boundaries, energy gaps, and order parameters are evaluated using the density matrix renormalization group method.
We discuss a novel mechanism for obtaining a spin-gap state through the creation of a coherent spin-orbital structure in systems with orbital degeneracy. Using the density matrix renormalization group, we calculate the phase diagram for a coupled spin-orbital model. We find that, in addition to ferromagnetic and power-law antiferromagnetic phases for spin and orbital degrees of freedom, this model has a gapless line extending from the ferromagnetic phase to the Bethe ansatz solvable SU(4) critical point, and a gapped phase with doubly degenerate ground states which form alternating spin and orbital singlets. The relevance to several recently discovered materials is discussed.
We study a one-dimensional spin-orbital model using both analytical and numerical methods. Renormalization group calculations are performed in the vicinity of a special integrable point in the phase diagram with SU(4)\mathrm{SU}(4)SU(4) symmetry. These indicate the existence of a gapless phase in an extended region of the phase diagram, missed in previous studies. This phase is SU(4)\mathrm{SU}(4)SU(4) invariant at low energies apart from the presence of different velocities for spin and orbital degrees of freedom. The phase transition into a gapped dimerized phase is in a generalized Kosterlitz-Thouless universality class. The phase diagram of this model is sketched using the density matrix renormalization group technique.
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We investigate the spin and orbital correlations of a superexchange model with spin S=1S=1S=1 and orbital L=1L=1L=1 relevant for 5d45{d}^{4}5d4 transition-metal Mott insulators [O. N. Meetei et al., Phys. Rev. B 91, 054412 (2015)], using exact diagonalization and density matrix renormalization group (DMRG). For spin-orbit coupling $\ensuremath{\lambda}=0$, the orbitals are in an entangled state that is decoupled from the spins. We find two phases with increasing $\ensuremath{\lambda}$: (I) the S2S2S2 phase with two peaks in the structure factor for $\ensuremath{\lambda}\ensuremath{\le}{\ensuremath{\lambda}}_{c1}\ensuremath{\approx}0.34J$ where JJJ is the ferromagnetic exchange; and, (II) the S1S1S1 phase for ${\ensuremath{\lambda}}_{c1}<\ensuremath{\lambda}\ensuremath{\le}{\ensuremath{\lambda}}_{c2}\ensuremath{\approx}1.2J$ with emergent antiferromagnetic correlations. Both S1S1S1 and S2S2S2 phases are shown to exhibit power-law correlations, indicative of a gapless spectrum. Upon increasing $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c2}$ leads to a product state of local spin-orbital singlets that exhibit exponential decay of correlations, indicative of a gapped phase. We obtain insights into the phases from the well-known Uimin-Lai-Sutherland model in an external field that provides an approximate description of our model within mean-field theory.
We investigate the quantum phases of a frustrated antiferromagnetic Heisenberg spin-1/2 model Hamiltonian on a Kagome-strip chain (KSC), a one-dimensional analogue of the Kagome lattice, and construct its phase diagram in an extended exchange parameter space. The isolated unit cell of this lattice comprises of five spin-1/2 particles, giving rise to several types of magnetic ground states in a unit cell: a spin-3/23/23/2 state as well as spin-1/21/21/2 states with and without additional degeneracies. We explore the ground state properties of the fully connected thermodynamic system using exact diagonalization and density matrix renormalization group methods, identifying several distinct quantum phases. All but one of the phases exhibit gapless spin excitations. The exception is a dimerized spin-gapped phase that covers a large part of the phase diagram and includes the uniformly exchange coupled system. We argue that this phase can be understood by perturbing around the limit of decoupled unit cells where each unit cell has six degenerate ground states. We use degenerate perturbation theory to obtain an effective Hamiltonian, a Kugel-Khomskii model with an anisotropic spin-one orbital degree of freedom, which helps explain the origin of dimerization.
We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0<n<1.75)(0<n<1.75)(0<n<1.75) electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling (n=1),(n=1),(n=1), the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities (n<1),(n<1),(n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1),(n>1),(n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling (n=2).(n=2).(n=2).