Exactly solvable Kitaev model in three dimensions

Mandal, Saroj; Surendran, Naveen

doi:10.1103/physrevb.79.024426

Cited by 193 publications

(269 citation statements)

References 32 publications

(41 reference statements)

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“…(ii) Material search and the experimental fingerprint of the mixed three-loop braiding statistics. There are several possible experimental realizations of Z 2 spin liquids, such as the so-called Kitaev spin liquid state in the lattices in β-and γ-Li 2 IrO 3 [85][86][87][88][89][90][91]. By further considering the unbroken Z 2 Ising symmetry, the resulting ground state should exhibit SET orders.…”

Section: Discussionmentioning

confidence: 99%

Symmetry enrichment in three-dimensional topological phases

Ning

Liu

2016

Phys. Rev. B

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While two-dimensional symmetry-enriched topological phases (SETs) have been studied intensively and systematically, three-dimensional ones are still open issues. We propose an algorithmic approach of imposing global symmetry Gs on gauge theories (denoted by GT) with gauge group Gg. The resulting symmetric gauge theories are dubbed "symmetry-enriched gauge theories" (SEG), which may be served as low-energy effective theories of three-dimensional symmetric topological quantum spin liquids. We focus on SEGs with gauge group Gg = ZN 1 × ZN 2 × · · · and on-site unitary symmetry group Gs = ZK 1 × ZK 2 × · · · or Gs = U(1) × ZK 1 × · · · . Each SEG(Gg, Gs) is described in the path integral formalism associated with certain symmetry assignment. From the path-integral expression, we propose how to physically diagnose the ground state properties (i.e., SET orders) of SEGs in experiments of charge-loop braidings (patterns of symmetry fractionalization) and the mixed multi-loop braidings among deconfined loop excitations and confined symmetry fluxes. From these symmetry-enriched properties, one can obtain the map from SEGs to SETs. By giving full dynamics to background gauge fields, SEGs may be eventually promoted to a set of new gauge theories (denoted by GT * ). Based on their gauge groups, GT * s may be further regrouped into different classes each of which is labeled by a gauge group G * g . Finally, a web of gauge theories involving GT, SEG, SET and GT * is achieved. We demonstrate the above symmetry-enrichment physics and the web of gauge theories through many concrete examples.

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Section: Discussionmentioning

confidence: 99%

Symmetry enrichment in three-dimensional topological phases

Ning

Liu

2016

Phys. Rev. B

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“…-Here we emphasize another advantage of MOFs: we can construct various complex geometric structures, not limited to the honeycomb lattice, by self-organization. In particular, three-dimensional (3D) generalizations of the Kitaev model are of great interest [32]. A realization in iridates has been reported but again with a magnetic ordering at low temperatures [33].…”

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confidence: 99%

Designing Kitaev Spin Liquids in Metal-Organic Frameworks

2017

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Kitaev's honeycomb lattice spin model is a remarkable exactly solvable model, which has a particular type of spin liquid (Kitaev spin liquid) as the ground state. Although its possible realization in iridates and α-RuCl3 has been vigorously discussed recently, these materials have substantial non-Kitaev direct exchange interactions and do not have a spin liquid ground state. We propose metal-organic frameworks (MOFs) with Ru 3+ (or Os 3+ ) forming the honeycomb lattice as promising candidates for a more ideal realization of Kitaev-type spin models where the direct exchange interaction is strongly suppressed. The great flexibility of MOFs allows generalization to other three-dimensional lattices, for potential realization of a variety of spin liquids such as a Weyl spin liquid.PhySH: Frustrated magnetism, Spin liquid, Quantum spin liquid, Organic compoundsIntroduction. -Quantum spin liquids, purported exotic states of quantum magnets where long-range magnetic orders are destroyed by quantum fluctuations, have been a central subject in quantum magnetism [1]. As an important theoretical breakthrough, Kitaev constructed a spin-1/2 model on the honeycomb lattice [2] with Ising interactions between spin components depending on bond orientations. Its exact solution demonstrates many intriguing properties such as fractionalized anyonic excitations. This model was later generalized to other lattices, including three-dimensional ones, still retaining the exact solvability [3]. In this paper, we call this type of model including various generalizations as Kitaev model, and its ground states as Kitaev spin liquids. Jackeli and Khaliullin [4] discovered that the "Kitaev interaction", namely bond-dependent Ising couplings, can be realized in a (111) honeycomb layer of iridates, i.e. the A 2 IrO 3 (A = Na, Li) structure, by the superexchange interaction through the oxygen ions due to the strong spin-orbit coupling of Ir 4+ in the Mott insulator limit (see also Ref.[5] for the itinerant limit).However, unfortunately, it turned out that iridates and related inorganic compounds, such as α-RuCl 3 [6], exhibit a conventional magnetic order at low enough temperatures and do not have a true spin liquid ground state. This is due to the non-Kitaev interactions, such as antiferromagnetic Heisenberg interaction, mainly coming from the direct exchange interaction between the metal ions [7]. While their finite-temperature properties still reflect the proximity to the Kitaev model [8] and thus are of great interest, the current situation calls for a more ideal realization of the Kitaev model in real materials, so that they exhibit spin liquid ground states.In this Letter, we propose such a possible realization of the Kitaev model in metal-organic frameworks (MOFs), crystalline materials consisting of metal ions and bridging organic ligands. Although MOF is a central subject in modern complex chemistry, MOFs have not attracted much attention in the context of magnetism. This is

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“…Spin-1/2 models of Kitaev type on the diamond lattice, and on other three-dimensional lattices have been constructed. 24,25,26 For these models, however, there is no phase analogous to the non-Abelian phase in the original Kitaev model, and the ground states discussed there have a vanishing winding number. Extensions of the spin 1/2 Kitaev model to models with 4-dimensional Hilbert space per site have been studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional topological phase on the diamond lattice

Ryu

2009

Phys. Rev. B

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An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice which exhibits both Abelian and non-Abelian phases, the model has two ("weak" and "strong" pairing) phases. In the weak pairing phase, the auxiliary Majorana hopping problem is in a topological superconducting phase characterized by a non-zero winding number introduced in A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 (2008) for the ensemble of Hamiltonians with both particle-hole and time-reversal symmetries. The topological character of the weak pairing phase is protected by a discrete symmetry.

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Exactly solvable Kitaev model in three dimensions

Cited by 193 publications

References 32 publications

Symmetry enrichment in three-dimensional topological phases

Symmetry enrichment in three-dimensional topological phases

Designing Kitaev Spin Liquids in Metal-Organic Frameworks

Three-dimensional topological phase on the diamond lattice

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