Three-dimensional topological phase on the diamond lattice

Ryu, Shinsei

doi:10.1103/physrevb.79.075124

Cited by 63 publications

(68 citation statements)

References 45 publications

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“…However, one might still be able to employ similar ideas to the ones used by Ryu in Ref. [40] to stabilize a non-trivial topological phase by introducing additional (orbital) degrees of freedom such that the augmented model can be reformulated as a free fermion model in symmetry class DIII. The latter does have a Z classification in three dimensions and, thus, allows for three dimensional analogs of the topological phase in the honeycomb model.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice

2014

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Motivated by the recent synthesis of β-Li2IrO3 -a spin-orbit entangled j = 1/2 Mott insulator with a threedimensional lattice structure of the Ir 4+ ions -we consider generalizations of the Kitaev model believed to capture some of the microscopic interactions between the Iridium moments on various trivalent lattice structures in three spatial dimensions. Of particular interest is the so-called hyperoctagon lattice -the premedial lattice of the hyperkagome lattice, for which the ground state is a gapless quantum spin liquid where the gapless Majorana modes form an extended two-dimensional Majorana Fermi surface. We demonstrate that this Majorana Fermi surface is inherently protected by lattice symmetries and discuss possible instabilities. We thus provide the first example of an analytically tractable microscopic model of interacting SU(2) spin-1/2 degrees of freedom in three spatial dimensions that harbors a spin liquid with a two-dimensional spinon Fermi surface.

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Section: Discussion and Outlookmentioning

confidence: 99%

Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice

2014

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“…Similarly, to define an exactly solvable spin model on the square lattice, we can take Dirac matrices and assign four components of the Dirac matrices to four distinct types of links that emanate from each site, as in the Kitaev-type model on the diamond lattice. 19 The sites on the square lattice are divided into A-and B-sublattices. Four links from a site on the A-sublattice are labeled, respectively, by µ = 0, 1, 2, 3 counterclockwise from the positive x-direction (Fig.…”

Section: A Hamiltonian With Nearest-neighbor Interactions Onlymentioning

confidence: 99%

“…15 Similarly, we can represent the two sets of Dirac matrices α µ and ζ µ with six Majorana fermions λ p (p = 0, · · · , 5): 14,[19][20][21] …”

Section: B Mapping To Majorana Fermion Modelmentioning

confidence: 99%

“…18 In this paper, we consider an extension of the Kitaev model on the square lattice that respects a TRS of some sort. Following similar extensions of the Kitaev model on the three-dimensional diamond lattice 19,20 and on the two-dimensional square lattice, 21 we consider two spin-1/2 degrees of freedom on each site that compose 4 × 4 Dirac matrices (γ matrices). Similarly to the original Kitaev model, we consider interactions among spins which are anisotropic in space and are designed in such a way that the model is solvable through the (Majorana) fermion representation of spins.…”

Section: Introductionmentioning

confidence: 99%

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Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

2012

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A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z2 topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the π-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z2 trivial and non-trivial phases.

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“…The emergence of fermions in three-dimensional bosonic systems has been demonstrated in various exactly solvable models [7][8][9]. Nevertheless, in all these models the underlying degrees of freedom are spin 3 2 or higher.…”

Section: Introductionmentioning

confidence: 98%

Fermions and nontrivial loop-braiding in a three-dimensional toric code

Mandal

Surendran

2014

Phys. Rev. B

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We study an exactly solvable toric code type of Hamiltonian in three dimensions, defined on the diamond lattice with spin-1/2 degrees of freedom at each site. The Hamiltonian is a sum of mutually commuting plaquette operators B p , all of which have eigenvalue +1 in the ground state. The excitations are "fluxes," which are plaquettes with B p = −1. Due to certain local kinematic constraints, fluxes form loops. The elementary flux-loop excitations are fermions, in contrast to other solvable spin-1/2 models in three dimensions, where the excitations are bosons. Furthermore, the flux loops braid nontrivially, giving rise to Abelian anyonlike statistics.

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Three-dimensional topological phase on the diamond lattice

Cited by 63 publications

References 45 publications

Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice

Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice

Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

Fermions and nontrivial loop-braiding in a three-dimensional toric code

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