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

Hermanns, Maria; Trebst, Simon

doi:10.1103/physrevb.89.235102

Cited by 111 publications

(123 citation statements)

References 45 publications

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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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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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“…Drawing significant attention is the A 2 IrO 3 family of layered honeycomb iridates [4][5][6][7][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]: these materials were first described by the Kitaev model [16] and later by the Heisenberg-Kitaev (HK) model [18], both of which host a Z 2 quantum spin liquid ground state first discovered in the context of Kitaev's exactly solvable spin-1/2 model [33]. Subsequently, similar exactly solvable spin models on several other two-dimensional (2D) and three-dimensional (3D) lattices were investigated [34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Theory of magnetic phase diagrams in hyperhoneycomb and harmonic-honeycomb iridates

2015

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Motivated by recent experiments, we consider a generic spin model in the j eff = 1/2 basis for the hyperhoneycomb and harmonic-honeycomb iridates. Based on microscopic considerations, the effect of an additional bond-dependent anisotropic spin exchange interaction ( ) beyond the Heisenberg-Kitaev model is investigated. We obtain the magnetic phase diagrams of the hyperhoneycomb and harmonic-honeycomb (H-1) lattices via a combination of the Luttinger-Tisza approximation, single-Q variational ansatz, and classical Monte Carlo simulated annealing. The resulting phase diagrams on both systems show the existence of incommensurate, noncoplanar spiral magnetic orders as well as other commensurate magnetic orders. The spiral orders show counterpropagating spiral patterns, which may be favorably compared to recent experimental results on both iridates. The parameter regimes of various magnetic orders and ordering wave vectors are quite similar in both systems. We discuss the implications of our work for recent experiments and also compare our results to those of the two-dimensional honeycomb iridate systems.PHYSICAL REVIEW B 91, 064407 (2015) single-Q ansatz minimization, and simulated annealing. We show that the hyperhoneycomb and H-1 lattices have similar phase diagrams, but differ from the phase diagram of the 2D honeycomb iridates in important ways. In addition to analogs of the ferromagnetic, antiferromagnetic, zigzag, and stripy phases of the HK model, we find a number of noncoplanar, counterpropagating spiral phases, multiple-Q states, and phases that have no direct analogs in the HK limit. We expound these phases and their static structure factors in Sec. V, thus providing results that can be compared with experiments. Finally, in Sec. VI, we discuss the relevance of our results to the newly discovered 3D-Li 2 IrO 3 compounds. II. STRUCTURE OF HYPERHONEYCOMBAND H-1 LATTICES 064407-2 THEORY OF MAGNETIC PHASE DIAGRAMS IN . . . PHYSICAL REVIEW B 91, 064407 (2015)

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“…On a honeycomb lattice, for instance, the leading anisotropic interactions take the form of the Kitaev model 3 , which is a rare example of exactly solvable models with nontrivial properties such as Majorana fermions and non-abelian statistics, and with potential links to quantum computing 4 . Realization of the Kitaev model is now being intensively sought out in a growing number of materials [7][8][9][10][11][12][13] , including 3D extensions of the honeycomb Li 2 IrO 3 , dubbed "hyper-honeycomb"…”

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confidence: 99%

Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3

et al. 2015

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Heisenberg interactions are ubiquitous in magnetic materials and have been prevailing in modeling and designing quantum magnets. Bonddirectional interactions 1-3 offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model 4 , which has a quantum spin liquid (QSL) as its exact ground state. Honeycomb iridates, A 2 IrO 3 (A=Na,Li), offer potential realizations of the Kitaev model, and their reported magnetic behaviors may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bonddirectional interactions remains indirect or conjectural. Here, we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na 2 IrO 3 and show that they lead to strong magnetic frustration. Diffuse magnetic xray scattering reveals broken spin-rotational symmetry even above T N , with the three spin components exhibiting nano-scale correlations along distinct crystallographic directions. This spinspace and real-space entanglement directly manifests the bond-directional interactions, provides the missing link to Kitaev physics in honeycomb iridates, and establishes a new design strategy toward frustrated magnetism.Iridium (IV) ions with pseudospin-1/2 moments form in Na 2 IrO 3 a quasi-two-dimensional (2D) honeycomb network, which is sandwiched between two layers of oxygen ions that frame edge-shared octahedra around the magnetic ions and mediate superexchange interactions between neighboring pseudospins (Fig. 1a). Owing to the particular spin-orbital structure of the pseudospin 5,6 , the isotropic part of the magnetic interaction is strongly suppressed in the 90• bonding geometry of the edgeshared octahedra 2,3 , thereby allowing otherwise subdominant bond-dependent anisotropic interactions to play the main role and manifest themselves at the forefront of magnetism. This bonding geometry, common to many transition-metal oxides, in combination with the pseudospin that arises from strong spin-orbit coupling gives rise to an entirely new class of magnetism beyond the traditional paradigm of Heisenberg magnets. On a honeycomb lattice, for instance, the leading anisotropic interactions take the form of the Kitaev model 3 , which is a rare example of exactly solvable models with nontrivial properties such as Majorana fermions and non-abelian statistics, and with potential links to quantum computing 4 . Realization of the Kitaev model is now being intensively sought out in a growing number of materials 7-13 , including 3D extensions of the honeycomb Li 2 IrO 3 , dubbed "hyper-honeycomb" 7 and "harmonichoneycomb" 8 , and 4d transition-metal analogs such as RuCl 3 12 and Li 2 RhO 3 13 . Although most of these are known to magnetically order at low temperature, they exhibit a rich array of magnetic structures including zigzag 14-16 , spiral 17 , and other more complex non-coplanar structures 18,19 that are predicted to occur in the vicinity of the Kitaev QSL phase [20][21][22][23] , which hosts man...

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

Cited by 111 publications

References 45 publications

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

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

Theory of magnetic phase diagrams in hyperhoneycomb and harmonic-honeycomb iridates

Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3

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