Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids

Jin, Hui-Ke; Natori, W. M. H.; Pollmann, F.; Knolle, J.

doi:10.48550/arxiv.2107.13364

Cited by 3 publications

(4 citation statements)

References 59 publications

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“…Rewriting the Kitaev model with those operators transforms it into a free-fermion problem. Here we similarly solve our model by using the Majorana representation of a spin-3/2 [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69]116].…”

Section: B Exact Solution For Arbitrary Field: Majorana Fermi Surface...mentioning

confidence: 99%

“…The dimers themselves may either represent singlets between spins on neighboring sites, or, be an intrinsic degree of freedom where the dimer constraint is enforced [17,49] or emerges from interactions [50][51][52]. Third, there are Kitaev spin models [29] including the honeycomb lattice S = 1/2 model and related constructions [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69], which can be solved by mapping to free-fermions. In all these previous cases, one is guaranteed a spin liquid phase from analytical arguments.…”

Section: Introductionmentioning

confidence: 99%

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Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids

Verresen¹,

Vishwanath²

2022

Preprint

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The exploration of quantum spin liquids (QSLs) has been guided by different approaches including the resonating valence bond (RVB) picture, deconfined lattice gauge theories and the Kitaev model. More recently, a spin liquid ground state was numerically established on the ruby lattice, inspired by the Rydberg blockade mechanism. Here we unify these varied approaches in a single parent Hamiltonian, in which local fluctuations of anyons stabilize deconfinement. The parent Hamiltonian is defined on kagomé triangles-each hosting four RVB-like states-and includes only Ising interactions and single-site transverse fields. In the weak-field limit, the ruby spin liquid and exactly soluble kagomé dimer models are recovered, while the strong-field limit reduces to the Kitaev honeycomb model, thereby unifying three seemingly different approaches to QSLs. We similarly obtain the chiral Yao-Kivelson model, honeycomb toric code and a new spin-1 quadrupolar Kitaev model. The last is shown to be in a QSL phase by a non-local mapping to the kagomé Ising antiferromagnet. We demonstrate various applications of our framework, including (a) an adiabatic deformation of the ruby lattice model to the exactly soluble kagomé dimer model, conclusively establishing the QSL phase in the former; and (b) demystifying the dynamical protocol for measuring off-diagonal strings in the Rydberg implementation of the ruby lattice spin liquid. More generally, we find an intimate connection between Kitaev couplings and the repulsive interactions used for emergent dimer models. For instance, we show how a spin-1/2 XXZ model on the ruby lattice encodes a Kitaev honeycomb model, providing a new route toward realizing the latter in cold-atom or solid-state systems. CONTENTSI. Introduction 1 II. Model 3 A. Emergent dimer model in a tensor product Hilbert space 3 B. Hamiltonian 6 C. Brief summary of the phase diagram(s) 8 III. Quantum liquids from e-anyon fluctuations 9 A. Weak-field limit: dimer liquid stabilizer model 9 B. Arbitrary field: duality to spin-1/2 transverse field Ising model on the kagomé lattice 9 C. Strong-field limit: spin-1 quadrupolar Kitaev model 10 IV. Quantum liquids from f -anyon fluctuations 11 A. Weak-field limit: distinct dimer liquid SETs 11 B. Exact solution for arbitrary field: Majorana Fermi surfaces and chiral non-Abelian Ising topological order 12 C. Strong-field limit: spin-1/2 Kitaev model 13 V. Applications 13 A. Adiabatically connecting ruby lattice spin liquid to solvable stabilizer Hamiltonian 13 B. The Hadamard transformation for a dimer model 14 C. A natural family of spin-1 Kitaev models 15 D. Kagomé dimer model as honeycomb toric code 16 VI. Local rewriting of spin-3/2 model as two-body spin-1/2 'grandparent' models 17 A. Ruby lattice 17 B. Star lattice 18 VII. Conclusions and future directions 19 Acknowledgments 21 References 21 A. Spin-3/2 Hilbert space 25 1. Algebra: Majoranas and bosonic operators 25 2. Z 3 isomorphisms 26 3. Z 2 Hadamard 26 4. Reduction to spin-1/2 26 5. Matrix representation 27 6. Connection t...

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Section: B Exact Solution For Arbitrary Field: Majorana Fermi Surface...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids

Verresen¹,

Vishwanath²

2022

Preprint

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“…Moreover, combining the density functional theory and the exact diagonalization (ED) calculation, the realization of the antiferromagnetic (AFM) Kitaev QSL was predicted for epitaxially strained monolayers of CrSiTe 3 and CrGeTe 3 with S = 3/2 moments [47,48]. Meanwhile, extensions of the Kitaev model to general S have been studied intensively in recent years [49][50][51][52][53][54][55][56][57][58][59][60][61]. It was proved that the ground state of the models is a QSL state for arbitrary S, where the spin correlations vanish beyond nearest neighbors [49].…”

Section: Introductionmentioning

confidence: 99%

Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models

Fukui¹,

Kato²,

Nasu³

et al. 2022

Preprint

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The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin S = 1/2 moments on a honeycomb lattice. In recent years, the model has been extended to higher S from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general S, especially in the presence of other additional interactions, which inevitably exist in candidate materials. Here we study the spin-S Kitaev-Heisenberg models by using an extension of the pseudofermion functional renormalization group method to general S. We show that, similar to the S = 1/2 case, the phase diagram for higher S contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases. We find, however, that the QSL phases shrink rapidly with increasing S, becoming vanishingly narrow for S ≥ 2, whereas the phase boundaries between the ordered phases remain almost intact. Our results provide a reference for the search of higher-S Kitaev materials.

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“…The semi-classical approximation is expected to hold for S 3/2. Moreover, DMRG calculations for S = 1 [30] and S = 3/2 [39] predict a gapless QSL ground state similar to S = 1/2 while TN calculations [34] predict a gapped QSL for S = 1 inline with the semi-classical findings [38]. For finite fields h > 0 and S ∈ {1/2, 1} there is convincing evidence by ED [31][32][33] and DMRG [28][29][30] for the presence of an intermediate region in the phase diagram between the gapped Kitaev phase at small (but finite) fields and the high-field polarized phase, which is also gapped but topologically trivial.…”

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confidence: 99%