Frustration in Systems with Orbital Degrees of Freedom

Brink, Jeroen van den; Nussinov, Zohar; Oleś, Andrzej M.

doi:10.1007/978-3-642-10589-0_23

Cited by 6 publications

(8 citation statements)

References 100 publications

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“…However, this is not the only possibility. If the electronic configuration of the transition metal ion is such that several orbital occupations are consistent with the crystal field environment, a situation referred to as orbital degeneracy [2], orbital fluctuations are likely to be much softer. In most cases known until recently, a cooperative Jahn-Teller distortion occurs, resulting in orbital order and gapped orbital excitations, but this needs not be the case a priori, and the search for situations in which orbitals remain fluctuating in the ground state has been very active over the past decade [3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Spin-Orbital Quantum Liquid on the Honeycomb Lattice

et al. 2012

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The main characteristic of Mott insulators, as compared to band insulators, is to host low-energy spin fluctuations. In addition, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in the majority of Mott insulators, spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the spin-orbital SUð4Þ symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breakinglattice or SUðNÞ-is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave function based on the -flux state of fermions on the honeycomb lattice at 1=4 filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides an interesting starting point to understanding the recently discovered spin-orbital-liquid behavior of Ba 3 CuSb 2 O 9 . The present results also suggest the choice of optical lattices with honeycomb geometry in the search for quantum liquids in ultracold four-color fermionic atoms.

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Section: Introductionmentioning

confidence: 99%

Spin-Orbital Quantum Liquid on the Honeycomb Lattice

et al. 2012

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“…Recent years have seen growing theoretical interest in systems exhibiting SU (N ) symmetry with the concomitant development of experimental research in condensed matter and atomic physics. On one hand, many electronic materials possess degenerate lowenergy atomic orbitals [1]: (approximate) SU (N ) symmetry emerging from this orbital degeneracy leads to interesting physics and is an active field of studies [2,3]. On the other hand, ultra-cold atom experiments started a new era to design systems with exact SU (N ) symmetry [4][5][6].…”

Section: Pacs Numbers:mentioning

confidence: 99%

Entanglement properties of the two-dimensional SU(3) Affleck-Kennedy-Lieb-Tasaki state

Gauthé

Poilblanc

2017

Phys. Rev. B

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Two-dimensional (spin-2) Affleck-Kennedy-Lieb-Tasaki (AKLT) type valence bond solids on the square lattice are known to be symmetry protected topological (SPT) gapped spin liquids [Shintaro Takayoshi, Pierre Pujol, and Akihiro Tanaka Phys. Rev. B 94, 235159 (2016)]. Using the projected entangled pair state (PEPS) framework, we extend the construction of the AKLT state to the case of SU (3), relevant for cold atom systems. The entanglement spectrum is shown to be described by an alternating SU (3) chain of "quarks" and "antiquarks", subject to exponentially decaying (with distance) Heisenberg interactions, in close similarity with its SU (2) analog. We discuss the SPT feature of the state.

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“…Spin-orbital interplay is one of the most important topics in the theory of frustrated magnetism [1][2][3][4][5] . When degenerate 3d orbitals in a transition metal oxide are partly filled, realistic superexchange includes both orbital and spin degrees of freedom that are strongly interrelated 6,7 .…”

Section: Introductionmentioning

confidence: 99%

Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation

Czarnik

Dziarmaga

2015

Phys. Rev. B

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We introduce a spin-orbital entangled (SOE) resonating valence bond (RVB) state on a square lattice of spins- . Like the standard RVB state, it is a superposition of nearest-neighbor hard-core coverings of the lattice by spin singlets, but adjacent singlets are favoured to have perpendicular orientations and, more importantly, an orientation of each singlet is entangled with orbitals' state on its two lattice sites. The SOE-RVB state can be represented by a projected entangled pair state (PEPS) with a bond dimension D = 4. This representation helps to reveal that the state is a superposition of striped coverings conserving a topological quantum number. The stripes are a critical quantum spin liquid. We propose a spinorbital Hamiltonian supporting a SOE-RVB ground state.

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Frustration in Systems with Orbital Degrees of Freedom

Cited by 6 publications

References 100 publications

Spin-Orbital Quantum Liquid on the Honeycomb Lattice

Spin-Orbital Quantum Liquid on the Honeycomb Lattice

Entanglement properties of the two-dimensional SU(3) Affleck-Kennedy-Lieb-Tasaki state

Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation

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