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Register a new userChiral and Critical Spin Liquids in Spin-$1/2$ Kagome Antiferromagnet
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The topological quantum spin liquids (SL) and the nature of quantum phase transitions between them have attracted intensive attentions for the past twenty years. The extended kagome spin-1/2 antiferromagnet emerges as the primary candidate for hosting both time reversal symmetry (TRS) preserving and TRS breaking SLs based on density matrix renormalization group simulations. To uncover the nature of the novel quantum phase transition between the SL states, we study a minimum XY model with the nearest neighbor (NN) ($J_{xy}$), the second and third NN couplings ($J_{2xy}=J_{3xy}=J_{xy}$). We identify the TRS broken chiral SL (CSL) with the turn on of a small perturbation $J_{xy}sim 0.06 J_{xy}$, which is fully characterized by the fractionally quantized topological Chern number and the conformal edge spectrum as the $ u=1/2$ fractional quantum Hall state. On the other hand, the NN XY model ($J_{xy}=0$) is shown to be a critical SL state adjacent to the CSL, characterized by the gapless spin singlet excitations and also vanishing small spin triplet excitations. The quantum phase transition from the CSL to the gapless critical SL is driven by the collapsing of the neutral (spin singlet) excitation gap. By following the evolution of entanglement spectrum, we find that the transition takes place through the coupling of the edge states with opposite chiralities, which merge into the bulk and become gapless neutral excitations. The effect of the NN spin-$z$ coupling $J_z$ is also studied, which leads to a quantum phase diagram with an extended regime for the gapless SL.
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We study the spin-$1/2$ Heisenberg model on the triangular lattice with the nearest-neighbor $J_1 > 0$, the next-nearest-neighobr $J_2 > 0$ Heisenberg interactions, and the additional scalar chiral interaction $J_{chi}(vec{S}_i times vec{S}_j) cdot vec{S}_k$ for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing $J_2$ ($J_2/J_1 leq 0.3$) and $J_{chi}$ ($J_{chi}/J_1 leq 1.0$) interactions, we establish a quantum phase diagram with the magnetically ordered $120^{circ}$ phase, stripe phase, and non-coplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a $ u = 1/2$ bosonic fractional quantum Hall state with possible spontaneous rotational symmetry breaking. By switching on the chiral interaction, we find that the previously identified spin liquid in the $J_1 - J_2$ triangular model ($0.08 lesssim J_2/J_1 lesssim 0.15$) shows a phase transition to the CSL phase at very small $J_{chi}$. We also compute spin triplet gap in both spin liquid phases, and our finite-size results suggest large gap in the odd topological sector but small or vanishing gap in the even sector. We discuss the implications of our results to the nature of the spin liquid phases.
We study the nearest neighbor $XXZ$ 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 suppport 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 $sxy = frac{1}{2}$ in the regime of $XY$ anisotropy. The Dzyaloshinkii-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 $XY$ 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.
We believe that a necessary first step in understanding the ground state properties of the spin-${scriptstylefrac{1}{2}}$ kagome Heisenberg antiferromagnet is a better understanding of this models very large number of low energy singlet states. A description of the low energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular when these turn on the delicate balance of many small energies. We demonstrate how this program would be implemented using the basis of spin-singlet dimerized states, though other bases that have been proposed may serve the same purpose. The quality of a basis is evaluated by its participation in all the low energy singlets, not just the ground state. From an experimental perspective, and again in light of the small energy scales involved, methods that can deliver all the low energy states promise more robust predictions than methods that only refine a fraction of these states.
We study the zero-temperature phase diagram of the spin-$frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical lattice-nematic phase that breaks rotational symmetry in real space through a first-order quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.
We introduce $mathrm{Nd_{3}Sb_{3}Mg_{2}O_{14}}$ with ideal kagome lattices of neodymium ions in ABC stacking. Thermodynamic measurements show a Curie-Weiss temperature of $Theta_{CW}=-0.12~$K, a Nd$^{3+}$ spin-1/2 Kramers doublet ground state, and a second order phase transition at $T_N=0.56(2)~$K. Neutron scattering reveals non-coplanar scalar chiral ${bf k} =0$ magnetic order with a correlation length exceeding 400 AA = 55 $a$ and an ordered moment of $1.79(5)~mu_B$. This order includes a canted ferromagnetic component perpendicular to the kagome planes favored by Dzyaloshinskii-Moriya interactions.
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