Chiral spin liquids at finite temperature in a three-dimensional Kitaev model

Kato, Yasuyuki; Kamiya, Yoshitomo; Nasu, Joji; Motome, Yukitoshi

doi:10.1103/physrevb.96.174409

Cited by 13 publications

(19 citation statements)

References 37 publications

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“…We do not see any anomaly except at T c in the T range studied here. This suggests that the hypernonagon Kitaev model at the isotropic point exhibits a single first-order transition to the CSL, similar to what is observed in its anisotropic limits 24 . However, given the peculiar structure of P (ε) in Fig.…”

Section: B Finite-temperature Phase Transitionsupporting

confidence: 69%

“…24, the SII configuration of Fig. 6(f) in the strong J x or J y limits 24 with a subextensive degeneracy, and the AF configuration in the strong J z limit 24 . Only the AFII phase of Fig.…”

Section: Ground State Phase Diagrammentioning

confidence: 94%

“…Guided by a previous study 24 concentrating on the limit of strong anisotropy in the exchange couplings, in which perturbation theory can be applied to derive an effective model, we further take into account the possibility that the low-T Z 2 gauge configuration exhibits a nonuniform flux pattern by considering exchange couplings beyond the anisotropic limits. This gives an even larger potential for thermodynamic phase transitions at which multiple symmetries are broken spontaneously and as such evade a conventional description in terms of the Landau-Ginzburg-Wilson paradigm.…”

Section: Arxiv:190710241v1 [Cond-matstr-el] 24 Jul 2019mentioning

confidence: 99%

“…Importantly, these two types of hexahedra form a distorted cubic lattice, which can be further deformed to a simple cubic lattice as shown in Fig. 2(b) 24,29 .…”

Section: A the Hypernonagon Latticementioning

confidence: 99%

“…In our hypernonagon case, the local constraint is enforced on each hexahedron in Fig. 2: the product of W p on the eight vertices is always equal to unity in all orange and purple hexahedra 24 .…”

Section: B Kitaev Model and Conserved Z2 Fluxesmentioning

confidence: 99%

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Chiral spin liquids with crystalline Z2 gauge order in a three-dimensional Kitaev model

et al. 2020

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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, which differ from their widely studied twodimensional counterparts, namely, they exhibit a crystalline ordering of the Z2 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 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 Z2 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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Section: B Finite-temperature Phase Transitionsupporting

confidence: 69%

“…24, the SII configuration of Fig. 6(f) in the strong J x or J y limits 24 with a subextensive degeneracy, and the AF configuration in the strong J z limit 24 . Only the AFII phase of Fig.…”

Section: Ground State Phase Diagrammentioning

confidence: 94%

Section: Arxiv:190710241v1 [Cond-matstr-el] 24 Jul 2019mentioning

confidence: 99%

“…Importantly, these two types of hexahedra form a distorted cubic lattice, which can be further deformed to a simple cubic lattice as shown in Fig. 2(b) 24,29 .…”

Section: A the Hypernonagon Latticementioning

confidence: 99%

Section: B Kitaev Model and Conserved Z2 Fluxesmentioning

confidence: 99%

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Chiral spin liquids with crystalline Z2 gauge order in a three-dimensional Kitaev model

et al. 2020

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Global constraints on Z2 fluxes in two different anisotropic limits of a hypernonagon Kitaev model

Kato

Kamiya

Nasu

et al. 2018

Physica B: Condensed Matter

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The Kitaev model is an exactly-soluble quantum spin model, whose ground state provides a canonical example of a quantum spin liquid. Spin excitations from the ground state are fractionalized into emergent matter fermions and Z 2 fluxes. The Z 2 flux excitation is pointlike in two dimensions, while it comprises a closed loop in three dimensions because of the local constraint for each closed volume. In addition, the fluxes obey global constraints involving (semi)macroscopic number of fluxes. We here investigate such global constraints in the Kitaev model on a three-dimensional lattice composed of nine-site elementary loops, dubbed the hypernonagon lattice, whose ground state is a chiral spin liquid. We consider two different anisotropic limits of the hypernonagon Kitaev model where the low-energy effective models are described solely by the Z 2 fluxes. We show that there are two kinds of global constraints in the model defined on a three-dimensional torus, namely, surface and volume constraints: the surface constraint is imposed on the even-odd parity of the total number of fluxes threading a two-dimensional slice of the system, while the volume constraint is for the even-odd parity of the number of the fluxes through specific plaquettes whose total number is proportional to the system volume. In the two anisotropic limits, therefore, the elementary excitation of Z 2 fluxes occurs in a pair of closed loops so as to satisfy both two global constraints as well as the local constraints.

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Projective symmetry group analysis of inelastic light scattering in Kitaev spin balls

Kimura

Yamamoto

2020

Phys. Rev. B

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Projective symmetry groups are applied to Raman observations of the Kitaev quantum spin liquids in spherical lattice geometries realized by Platonic and Archimedean polyhedra. Parton single excitations in Kitaev spin polyhedra are characterized by double-valued irreducible representations of their belonging projective symmetry groups, whereas parton geminate excitations relevant to Raman scattering are decomposed into single-valued irreducible representations of the corresponding point symmetry groups. We combine a standard point symmetry group analysis of the Loudon-Fleury vertices and an elaborate projective symmetry group analysis of itinerant spinons against the ground gauge fields to reveal hidden selection rules for Raman scattering in Z 2 spin liquids.

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Chiral spin liquids at finite temperature in a three-dimensional Kitaev model

Cited by 13 publications

References 37 publications

Chiral spin liquids with crystalline Z2 gauge order in a three-dimensional Kitaev model

Chiral spin liquids with crystalline Z2 gauge order in a three-dimensional Kitaev model

Global constraints on Z2 fluxes in two different anisotropic limits of a hypernonagon Kitaev model

Projective symmetry group analysis of inelastic light scattering in Kitaev spin balls

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