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Chiral, Double-semion Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets

Yin-Chen He, Yan Chen

Published Jul 10, 2014• 0 citations
OpenAlex

Abstract

By using the density matrix renormalization group, we study the spin-liquid phases of spin-$1/2$ 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 $S^z$ interaction) and XY (zero $S^z$ 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-$1/2$ kagome antiferromagnetic Heisenberg model.

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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.
By using the density matrix renormalization group approach, we study spin-liquid phases of spin-1/2 XXZ kagome antiferromagnets. We find that the emergence of the spin-liquid phase is independent of the anisotropy of the XXZ interaction. In particular, the two extreme limits-the Ising (a strong S^{z} interaction) and the XY (zero S^{z} interaction)-host the same spin-liquid phases as the isotropic Heisenberg model. Both a time-reversal-invariant spin liquid and a chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show that they evolve continuously into each other by tuning the second- and the third-neighbor interactions. And last, we discuss possible implications of our results for the nature of spin liquid in nearest-neighbor XXZ kagome antiferromagnets, including the nearest-neighbor spin-1/2 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 is a chiral spin liquid. Combining the density matrix renormalization group method with 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 of the phase diagram. We characterize the nature of the ground state by computing energy derivatives, revealing the ground-state degeneracy arising from the spontaneous breaking of the 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\sqrt{3}\times \sqrt{3}3​×3​ 3 × 3 magnetically ordered phase and two valence-bond crystal phases.
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 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.
Despite its deceptive simplicity, few concepts have more fundamental implications than chirality, from the therapeutic activity of drugs to the fundamental forces of nature. In magnetic materials, chirality gives rise to unconventional phenomena such as the anomalous Hall effect and multiferroicity, taking an enhanced flavour in the so-called spin-liquid phases where magnetic disorder prevails. Kagome systems sit at the crossroad of these ideas. Motivated by the recent synthesis of rare-earth kagome materials and the progresses in optical-lattice experiments, we bring together an entire network of spin liquids with anisotropic and Dzyaloshinskii-Moriya interactions. This network revolves around the Ising antiferromagnet and ends on (ferromagnetic) chiral spin liquids with spontaneously broken time-reversal symmetry. As for the celebrated Heisenberg antiferromagnet, it now belongs to a triad of equivalently disordered phases. The present work provides a unifying theory of kagome spin liquids with time-reversal invariant nearest-neighbour Hamiltonians.