Anyonic loops in three-dimensional spin liquid and chiral spin liquid

Si, Tieyan; Yu, Yue

doi:10.1016/j.nuclphysb.2008.06.009

Cited by 36 publications

(35 citation statements)

References 36 publications

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“…This result is rigorously established by an exact analytical solution of the spin model, which can be cast into a free fermion system by Majorana fermionization, thus employing the same powerful techniques that have already allowed the solution of the Kitaev model on other trivalent lattices [3,14,19].…”

Section: Introductionmentioning

confidence: 97%

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: Introductionmentioning

confidence: 97%

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

2014

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“…By now, many properties of the Kitaev model have been studied, including static [2] and dynamic [4,5] spin correlations as well as the physics of isolated defects [6][7][8]. In addition, variants of the Kitaev model on other lattices, both in two [9][10][11][12][13] and three [14][15][16] space dimensions, have been discussed. In all cases, the most popular analytical treatment of the compass interactions utilizes a Majorana representation of spins.…”

Section: Introductionmentioning

confidence: 99%

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

Zschocke

Vojta

2015

Phys. Rev. B

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Kitaev's compass model on the honeycomb lattice realizes a spin liquid whose emergent excitations are dispersive Majorana fermions and static Z 2 gauge fluxes. We discuss the proper selection of physical states for finite-size simulations in the Majorana representation, based on a recent paper by F. L. Pedrocchi, S. Chesi, and D. Loss [Phys. Rev. B 84, 165414 (2011)]. Certain physical observables acquire large finite-size effects, in particular if the ground state is not fermion-free, which we prove to generally apply to the system in the gapless phase and with periodic boundary conditions. To illustrate our findings, we compute the static and dynamic spin susceptibilities for finite-size systems. Specifically, we consider random-bond disorder (which preserves the solubility of the model), calculate the distribution of local flux gaps, and extract the NMR line shape. We also predict a transition to a random-flux state with increasing disorder.

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“…Recently physical realizations of the spin-1/2 Kitaev model have been proposed in optical lattice systems [14] and in quantum circuits [15]. Variants of the model have also been studied in two dimensions [16][17][18][19][20][21][22][23][24], three dimensions [25,26] and also on quasi-one-dimensional lattices [27][28][29]. Finally, the spin-S Kitaev model has been studied in the large S limit using spin wave theory [30], and the classical version of the Kitaev model has been studied at finite temperatures using analytical and Monte Carlo techniques [31].…”

Section: Introductionmentioning

confidence: 99%

Spin-1 Kitaev model in one dimension

et al. 2010

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We study a one-dimensional version of the Kitaev model on a ring of size N , in which there is a spin S > 1/2 on each site and the Hamiltonian is J n S x n S y n+1 . The cases where S is integer and half-odd-integer are qualitatively different. We show that there is a Z2 valued conserved quantity Wn for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2 N sectors, of unequal sizes. The number of states in most of the sectors grows as d N , where d depends on the sector. The largest sector contains the ground state, and for this sector, for S = 1, d = ( √ 5 + 1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term λ n Wn, and show that this has gapless excitations in the range λ

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Anyonic loops in three-dimensional spin liquid and chiral spin liquid

Cited by 36 publications

References 36 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

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

Spin-1 Kitaev model in one dimension

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