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arXiv:1503.03389 · Physical Review B

Nature of chiral spin liquids on the kagome lattice

Alexander Wietek, Antoine Sterdyniak, Andreas Martin Läuchli

Published Sep 14, 2015• 91 citations
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Abstract

We investigate the stability and the nature of the chiral spin liquids which were recently uncovered in extended Heisenberg models on the kagome lattice. Using a Gutzwiller projected wave function approach, i.e., a parton construction, we obtain large overlaps with ground states of these extended Heisenberg models. We further suggest that the appearance of the chiral spin liquid in the time-reversal invariant case is linked to a classical transition line between two magnetically ordered phases.

DOI
10.1103/physrevb.92.125122

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Motivated by recent experiments on the Heisenberg S=1/2S=1/2S=1/2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional phase of decoupled antiferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.
We study the quantum phase diagram of the spin-1/21/21/2 Heisenberg model on the kagome lattice with first-, second-, and third-neighbor interactions J1,J2{J}_{1},{J}_{2}J1​,J2​, and J3{J}_{3}J3​ by means of density matrix renormalization group. For small J2{J}_{2}J2​ and J3{J}_{3}J3​, this model sustains a time-reversal invariant quantum spin-liquid phase. With increasing J2{J}_{2}J2​ and J3{J}_{3}J3​, we find in addition a q=(0,0)q=(0,0)q=(0,0) N\'eel phase, a chiral spin-liquid phase, an apparent valence-bond crystal phase, and a complex noncoplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time-reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first-order phase transition. The transitions from the chiral spin liquid to both the q=(0,0)q=(0,0)q=(0,0) phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions.
We study the nearest-neighbor XXZXXZXXZ Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: (a) a chirality term, (b) a Dzyaloshinski-Moriya term, and (c) a ring-exchange type term on the bowties of the kagome lattice, and inquire if they can support chiral spin liquids as ground states. The method used to study these Hamiltonians is a flux attachment transformation that maps the spins on the lattice to fermions coupled to a Chern-Simons gauge field on the kagome lattice. This transformation requires us to consistently define a Chern-Simons term on the kagome lattice. We find that the chirality term leads to a chiral spin liquid even in the absence of an uniform magnetic field, with an effective spin Hall conductance of ${\ensuremath{\sigma}}_{xy}^{s}=\frac{1}{2}$ in the regime of XYXYXY anisotropy. The Dzyaloshinski-Moriya term also leads a similar chiral spin liquid but only when this term is not too strong. An external magnetic field also has the possibility of giving rise to additional plateaus which also behave like chiral spin liquids in the XYXYXY regime. Finally, we consider the effects of a ring-exchange term and find that, provided its coupling constant is large enough, it may trigger a phase transition into a chiral spin liquid by the spontaneous breaking of time-reversal invariance.
By using the density matrix renormalization group, we study the spin-liquid phases of spin-1/21/21/2 XXZ kagome antiferromagnets. We find that the emergence of spin liquid phase does not depend on the anisotropy of the XXZ interaction. In particular, the two extreme limits---Ising (strong SzS^zSz interaction) and XY (zero SzS^zSz interaction)---host the same spin-liquid phases as the isotropic Heisenberg model. Both the time-reversal-invariant spin liquid and the chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show they evolve continuously into each other by tuning the second- and third-neighbor interactions. To understand the continuous phase transition between these two spin liquids, we construct a phenomenological theory, and propose the double-semion spin liquid as the candidate ground state of nearest-neighbor XXZ kagome antiferromagnets, including the most studied nearest-neighbor spin-1/21/21/2 kagome antiferromagnetic Heisenberg model.
Abstract The nature of the ground state for the S = 1/2 kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state might be a chiral spin liquid. Combining the density matrix renormalization group method and analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region. We characterize the nature of the ground state by computing energy derivatives, revealing ground-state degeneracy arising from spontaneous breaking of time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a √3 × √3 magnetically ordered phase and two valence-bond crystal phases.
We investigate the extended Heisenberg model on the kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor superexchanges are considered, we find that a gapped spin liquid described by nontrivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with a C=1/2C=1/2C=1/2 fractionalized Chern number.