| 1. |
- Eschmann, Tim, et al.
(author)
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Thermodynamic classification of three-dimensional Kitaev spin liquids
- 2020
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In: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 102:7
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Journal article (peer-reviewed)abstract
- In the field of frustrated magnetism, Kitaev models provide a unique framework to study the phenomena of spin fractionalization and emergent lattice gauge theories in two and three spatial dimensions. Their ground states are quantum spin liquids, which can typically be described in terms of a Majorana band structure and an ordering of the underlying Z(2) gauge structure. Here we provide a comprehensive classification of the "gauge physics" of a family of elementary three-dimensional Kitaev models, discussing how their thermodynamics and ground state order depends on the underlying lattice geometry. Using large-scale, sign-free quantum Monte Carlo simulations we show that the ground-state gauge order can generally be understood in terms of the length of elementary plaquettes-a result which extends the applicability of Lieb's theorem to lattice geometries beyond its original scope. At finite temperatures, the proliferation of (gapped) vison excitations destroys the gauge order at a critical temperature scale, which we show to correlate with the size of vison gap for the family of three-dimensional Kitaev models. We also discuss two notable exceptions where the lattice structure gives rise to "gauge frustration" or intertwines the gauge ordering with time-reversal symmetry breaking In a more general context, the thermodynamic gauge transitions in such 3D Kitaev models are one of the most natural settings for phase transitions beyond the standard Landau-Ginzburg-Wilson paradigm.
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| 2. |
- Mishchenko, Petr A., et al.
(author)
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Chiral spin liquids with crystalline Z(2) gauge order in a three-dimensional Kitaev model
- 2020
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In: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 101:4
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Journal article (peer-reviewed)abstract
- Chiral spin liquids (CSLs) are time-reversal-symmetry-breaking ground states of frustrated quantum magnets that show no long-range magnetic ordering but instead exhibit topological order and fractional excitations. Their realization in simple and tractable microscopic models has, however, remained an open challenge for almost two decades until it was realized that Kitaev models on lattices with odd-length loops are natural hosts for such states, even in the absence of a time-reversal-symmetry-breaking magnetic field. Here we report on the formation of CSLs in a three-dimensional Kitaev model on a hypernonagon lattice composed of nine-site loops, which differ from their widely studied two-dimensional counterparts; namely, they exhibit a crystalline ordering of the Z(2) gauge fluxes and thereby break some of the underlying lattice symmetries. We study the formation of these unconventional CSLs via extensive quantum Monte Carlo simulations and demonstrate that they are separated from the featureless paramagnet at high temperatures by a single first-order phase transition at which both time-reversal and lattice symmetries are simultaneously broken. Using variational approaches for the ground state, we explore the effect of varying the Kitaev couplings and find at least five distinct CSL phases, all of which possess crystalline ordering of the Z(2) gauge fluxes. For some of these phases, the complementary itinerant Majorana fermions exhibit gapless band structures with topological features such as Weyl nodes or nodal lines in the bulk and Fermi arc or drumhead surface states.
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