Heisenberg-Kitaev model on the hyperhoneycomb lattice

Lee, Eric Kin-Ho; Schaffer, Robert; Bhattacharjee, Subhro; Kim, Yong Baek

doi:10.1103/physrevb.89.045117

Cited by 103 publications

(153 citation statements)

References 44 publications

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“…(ii) Material search and the experimental fingerprint of the mixed three-loop braiding statistics. There are several possible experimental realizations of Z 2 spin liquids, such as the so-called Kitaev spin liquid state in the lattices in β-and γ-Li 2 IrO 3 [85][86][87][88][89][90][91]. By further considering the unbroken Z 2 Ising symmetry, the resulting ground state should exhibit SET orders.…”

Section: Discussionmentioning

confidence: 99%

Symmetry enrichment in three-dimensional topological phases

Ning

Liu

2016

Phys. Rev. B

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While two-dimensional symmetry-enriched topological phases (SETs) have been studied intensively and systematically, three-dimensional ones are still open issues. We propose an algorithmic approach of imposing global symmetry Gs on gauge theories (denoted by GT) with gauge group Gg. The resulting symmetric gauge theories are dubbed "symmetry-enriched gauge theories" (SEG), which may be served as low-energy effective theories of three-dimensional symmetric topological quantum spin liquids. We focus on SEGs with gauge group Gg = ZN 1 × ZN 2 × · · · and on-site unitary symmetry group Gs = ZK 1 × ZK 2 × · · · or Gs = U(1) × ZK 1 × · · · . Each SEG(Gg, Gs) is described in the path integral formalism associated with certain symmetry assignment. From the path-integral expression, we propose how to physically diagnose the ground state properties (i.e., SET orders) of SEGs in experiments of charge-loop braidings (patterns of symmetry fractionalization) and the mixed multi-loop braidings among deconfined loop excitations and confined symmetry fluxes. From these symmetry-enriched properties, one can obtain the map from SEGs to SETs. By giving full dynamics to background gauge fields, SEGs may be eventually promoted to a set of new gauge theories (denoted by GT * ). Based on their gauge groups, GT * s may be further regrouped into different classes each of which is labeled by a gauge group G * g . Finally, a web of gauge theories involving GT, SEG, SET and GT * is achieved. We demonstrate the above symmetry-enrichment physics and the web of gauge theories through many concrete examples.

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Section: Discussionmentioning

confidence: 99%

Symmetry enrichment in three-dimensional topological phases

Ning

Liu

2016

Phys. Rev. B

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“…29,36,37 We leave the study of the other interaction terms discussed in connection with the iridates, such as the Kitaev interaction, 12,13,25,26 to future work. An inclusion of such a term will introduce additional spin-triplet pairing.…”

Section: Model For Superconductivitymentioning

confidence: 99%

“…In the past few years, there have been many experimental and theoretical studies of these materials in the context of magnetism, with the hope of finding a quantum spin liquid ground state. 22,[24][25][26][27][28][29][30] Other proposals of exotic physics on these lattices include a Weyl spin liquid 31 and line nodes. 32 Despite the large interest in the strongly correlated ground state of the undoped harmonic honeycomb materials, the possibility for superconductivity upon doping has so far not been explored.…”

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confidence: 99%

From chirald-wave to nodal line superconductivity in the harmonic honeycomb lattices

2016

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Motivated by the recent realization of the three-dimensional hyperhoneycomb and stripyhoneycomb lattices in lithium iridate (Li2IrO3), we study the possible spin-singlet superconducting states on the whole series of harmonic honeycomb lattices. Beginning with an isolated out-of-plane twist making the honeycomb lattice three-dimensional, we find that the chiral d ± id state, well-known from the honeycomb lattice, is realized in the largest members of the series at low to intermediate doping. Along the twist, four chiral edge states form a two-dimensional dispersive band. Reducing the distance between the twists to form the smaller members of the harmonic honeycomb lattices, the degeneracy between the d-wave states is lifted, which finally destroys the chiral state. By analyzing the hyper-and stripyhoneycomb lattices and generalizing using the D 2h point group of all the harmonic honeycomb lattices, we show that the superconducting state often belongs to the trivial irreducible representation. This state has nodal lines at low to intermediate doping, which is possible because the full lattice symmetry allows sign changes between different sets of bonds. We also find time-reversal symmetry broken states, which are either fully gapped or feature nodal points, in certain parts of the phase diagram. Finally, we draw a comparison between the states classified in terms of the D 2h symmetries and those observed on the D 6h honeycomb lattice.

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“…Indeed, the solid phase (magnetically ordered phase) is accessible in the context of the present 3D Kitaev model, by considering additional interactions which favor a magnetic order, such as the Heisenberg exchange interaction [30,31]. The detailed study of the magnetic three states of matter, liquid, gas, and solid, will provide a new insight in the research area of magnetism.…”

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confidence: 99%

Vaporization of Kitaev Spin Liquids

2014

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Quantum spin liquid is an exotic quantum state of matter in magnets. This state is a spin analogue of the liquid helium which does not solidify down to the lowest temperature due to strong quantum fluctuations. In conventional fluids, liquid and gas possess the same symmetry and adiabatically connect to each other by bypassing the critical end point. We find that the situation is qualitatively different in quantum spin liquids realizing in a three-dimensional Kitaev model; both gapless and gapped quantum spin liquid phases at low temperatures are always distinguished from the high-temperature paramagnet (spin gas) by a phase transition. The results challenge common belief that the absence of thermodynamic singularity down to the lowest temperature is a symptom of a quantum spin liquid. Tremendous efforts have been devoted to the realization of QSL, and several candidates were recently discovered in quasi two-dimensional (2D) and three-dimensional (3D) compounds [2][3][4][5][6]. In these compounds, QSL is usually identified by the absence of anomalies in the temperature (T ) dependence of physical quantities. Namely, it is implicitly supposed that a spin "gas" corresponding to the high-T paramagnet is adiabatically connected with QSL. This common belief lends itself to the fact that liquid and gas are adiabatically connected with each other in conventional fluids. In fact, the concept of QSL was originally introduced on the analogy of helium in which the liquid phase is retained down to the lowest T due to strong quantum fluctuations [7].In general, however, liquid and gas are distinguished by a discontinuous phase transition, while the adiabatic connection between them is guaranteed beyond the critical end point. Hence, a phase transition separating paramagnet and QSL is also expected. Nevertheless, the theory for thermodynamics of QSLs has not been seriously investigated thus far, and a thermodynamic phase transition for QSL has not ever been reported beyond the mean-field approximation. It is highly nontrivial whether a liquid-gas transition exists in quantum spin systems in a similar manner to that in conventional fluids. The issue is critical not only for theoretical understanding of QSLs but also for the interpretation of existing and forthcoming experiments.The lack of theoretical investigation of thermodynamics of QSLs is mainly due to the following two difficulties. One is the scarcity of well-identified QSLs. It is hard to characterize QSL because spatial quantum entanglement and many-body effects are essential for realizing QSL [8, 9]. The other difficulty lies in less choice of effective theoretical tools. Any biased approximation might be harmful for taking into account strong quantum and thermal fluctuations.In this Letter, we solve these difficulties by investigating a 3D extension of the Kitaev model [10], which sup- ports well-identified QSLs as the exact ground states [11] by applying an unbiased quantum Monte Carlo (MC) simulation without negative sign problem. By clarifying the phase diagram ...

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Heisenberg-Kitaev model on the hyperhoneycomb lattice

Cited by 103 publications

References 44 publications

Symmetry enrichment in three-dimensional topological phases

Symmetry enrichment in three-dimensional topological phases

From chirald-wave to nodal line superconductivity in the harmonic honeycomb lattices

Vaporization of Kitaev Spin Liquids

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