Quantum trimer models and topological SU(3) spin liquids on the kagome lattice

Jandura, Sven; Iqbal, Mohsin; Schuch, Norbert

doi:10.1103/physrevresearch.2.033382

Cited by 8 publications

(4 citation statements)

References 30 publications

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“…Future directions include attempting to generalize the construction to trimers [48] and n-mers, as well as ringexchange moves that involve larger number of plaquettes due to additional constraints from longer range interactions [49]. Furthermore, it would be useful for characterizing the nature of Hilbert space fragmentation to determine the number of Krylov subspaces when a certain necessary move is absent [17].…”

Section: Discussionmentioning

confidence: 99%

Ergodic Archimedean dimers

Røising¹,

Zhang²

2023

Preprint

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We study perfect matchings, or close-packed dimer coverings, of finite sections of Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.

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Section: Discussionmentioning

confidence: 99%

Ergodic Archimedean dimers

Røising¹,

Zhang²

2023

Preprint

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show abstract

“…Future directions include attempting to generalize the construction to trimers [46] and n-mers, as well as ring-exchange moves that involve larger number of plaquettes due to additional constraints from longer range interactions [47]. Furthermore, it would be useful for characterizing the nature of Hilbert space fragmentation to determine the number of Krylov subspaces when a certain necessary move is absent [17].…”

Section: Discussionmentioning

confidence: 99%

Ergodic Archimedean dimers

Røising¹,

Zhang

2023

SciPost Phys. Core

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We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.

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“…Can this be extended to other cases? Here a natural starting point is the study of other types of constrained models and their related deconfined phases [130][131][132][133].…”

Section: Discussionmentioning

confidence: 99%

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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Quantum trimer models and topological SU(3) spin liquids on the kagome lattice

Cited by 8 publications

References 30 publications

Ergodic Archimedean dimers

Ergodic Archimedean dimers

Ergodic Archimedean dimers

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

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