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arXiv:1206.3216 · Acta Physica Polonica A

Spin-Orbital Liquid on a Triangular Lattice

Andrzej M. Oleś, Jiří Chaloupka

Published May 1, 2012• 3 citations
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Abstract

Using Lanczos exact diagonalization of nite clusters we demonstrate that the spin-orbital d 1 model for triply degenerate t2g orbitals on a triangular lattice provides an example of a spin-orbital liquid ground state.We also show that the spin-orbital liquid involves entangled valence bond states which violate the GoodenoughKanamori rules, and modify eective spin exchange constants.

DOI
10.12693/aphyspola.121.1026

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Using Lanczos exact diagonalization of nite clusters we demonstrate that the spin-orbital d 1 model for triply degenerate t2g orbitals on a triangular lattice provides an example of a spin-orbital liquid ground state.We also show that the spin-orbital liquid involves entangled valence bond states which violate the GoodenoughKanamori rules, and modify eective spin exchange constants.
We investigate the ground state of the d1{d}^{1}d1 spin-orbital model for triply degenerate t2g{t}_{2g}t2g​ orbitals on a triangular lattice that unifies intrinsic frustration of spin and orbital interactions with geometrical frustration. Using full or Lanczos exact diagonalization of finite clusters, we establish that the ground state of the spin-orbital model that interpolates between superexchange and direct exchange interactions on the bonds is characterized by valence-bond correlations. In the absence of Hund's exchange the model describes a competition between various possible valence-bond states. By considering the clusters with open boundary conditions we demonstrate that orbital interactions are always frustrated, but this frustration is removed by pronounced spin singlet correlations that coexist with dimer orbital correlations supporting them. Such local configurations contribute to the disordered ground states found for the clusters with periodic boundary conditions that interpolate between a highly resonating, dimer-based, entangled spin-orbital liquid phase and a valence-bond state with completely static spin-singlet states. We argue that these states are also realized for the infinite lattice and anticipate that pronounced transitions between different regimes found for particular geometries will turn out to smooth crossovers in the properties of the spin-orbital liquid in the thermodynamic limit. Finally, we provide evidence that the resonating spin-orbital liquid phase involves entangled states on the bonds. In such a phase classical considerations based on the mean-field theory cannot be used, spin exchange interactions do not determine spin bond correlations, and quantum fluctuations play a crucial role in the ground states and magnetic transitions.
We performed an exact diagonalization study of the spin-liquid phase of the multiple-spin exchange model on a triangular lattice. It is characterized by no N\'eel long-range order, short-ranged magnetic correlations, and a spin gap. We found no long-range order in any local order parameter we investigated (chiral, dimer, etc.) The probable asymptotic ground-state degeneracy is discussed. We argue that it could be of topological origin and that the system is probably not a chiral spin liquid. A possible relation to the Affleck-Kennedy-Lieb-Tasaki, or valence-bond solid phase is discussed.
The spin-orbital model for triply degenerate t2g{t}_{2g}t2g​ electrons on a triangular lattice has been shown to be dominated by dimers. The phase diagram contains both strongly resonating, compound spin-orbital dimer states and quasistatic, spin-singlet valence-bond (VB) states. To elucidate the nature of the true ground state in these different regimes, the model is mapped to a number of quantum dimer models (QDMs), each of which has three dimer colors. The generic multicolored QDM, illustrated for the two- and three-color cases, possesses a topological color structure, ``color vison'' excitations, and broad regions of resonating VB phases. The specific models are analyzed to gain further insight into the likely ground states in the superexchange and direct-exchange limits of the electronic Hamiltonian, and they suggest a strong tendency toward VB order in all cases.
Using Lanczos exact diagonalization (ED), we study the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model with the four-spin ring-exchange interaction Jr{J}_{r}Jr​ on a triangular lattice. We mainly use the level spectroscopic technique of two 36-site tori to investigate the ground-state phase diagram, and further characterize phases by spin, dimer, and chiral correlation functions. The ground state has rich phases including several magnetic-ordered phases like the zigzag phase and tetrahedral phase, as well as several novel nonmagnetic phases, some of which exhibit valence bond solid behavior in their dimer correlation functions. However, we do not find direct evidence of a quantum spin liquid phase with spinon Fermi surface in this model. Our results can give a better understanding of the ground-state properties of the triangular Heisenberg model with ring-exchange interaction and help to understand the relevant triangular materials.
The ground state phase of spin-1/2 J_1-J_2 antiferromagnetic Heisenberg model on square lattice in the maximally frustrated regime (J_2 ~ 0.5J_1) has been debated for decades. Here we study this model by using a recently proposed novel numerical method - the cluster update algorithm for tensor product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with the state of art exact diagonalization study, and the energy differences between these two studies are of the order of 10^{-3}J_1 per site. At the largest bond dimension available D (D=9), we find a paramagnetic ground state without any valence bond solid order in the thermodynamic limit in the range of 0.5 < J_2/J_1 < 0.6, which implies the emergence of a spin-liquid phase. Furthermore, we investigate the topologically ordered nature of such a spin-liquid phase by measuring a nonzero topological entanglement entropy.
We argue for the existence of a liquid ground state in a class of square lattice models of orbitally degenerate insulators. Starting with the SU(4)-symmetric Kugel-Khomskii model, we utilize a Majorana Fermion representation of spin-orbital operators to access unusual phases. Variational wave functions of candidate liquid phases are thus obtained, whose properties are evaluated using variational Monte Carlo. These states are disordered and are found to have excellent energetics and ground state overlap (>40(>40%)(>40 when compared with exact diagonalization on 16-site clusters. We conclude that these are spin-orbital liquid ground states with emergent nodal fermions and Z2{\text{Z}}_{2}Z2​ gauge fields. Connections to spin-3/2 cold-atom systems and properties in the absence of SU(4) symmetry are briefly discussed.