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Register a new userCoexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
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We study the ground-state properties of a spin-1 Heisenberg model on the square lattice with the first and second nearest-neighbor antiferromagnetic couplings $J_1$, $J_2$ and a three-spin scalar chirality term $J_chi$. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state by the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Our results not only establish a rare example of non-Abelian spin liquids in simple spin systems, but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions.
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We extend the scope of Kitaev spin liquids to non-Archimedean lattices. For the pentaheptite lattice, which results from the proliferation of Stone-Wales defects on the honeycomb lattice, we find an exactly solvable non-Abelian chiral spin liquid with spontaneous time reversal symmetry breaking due to lattice loops of odd length. Our findings call for potential extensions of exact results for Kitaev models which are based on reflection positivity, which is not fulfilled by the pentaheptite lattice. We further elaborate on potential realizations of our chiral spin liquid proposal in strained $alpha$-RuCl$_3$.
We establish the existence of a chiral spin liquid (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle. The CSL state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSLs separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial (Chern number $pm 1$) CSL obey non-Abelian statistics.
We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3)_1$ (or, equivalently, $SU(2)_2$) field theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study we observe a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.
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.
One of the key questions concerning frustrated lattices that has lately emerged is the role of disorder in inducing spin-liquid-like properties. In this context, the quantum kagome antiferromagnets YCu$_3$(OH)$_6$Cl$_3$, which has been recently reported as the first geometrically perfect realization of the kagome lattice with negligible magnetic/non-magnetic intersite mixing and a possible quantum-spin-liquid ground state, is of particular interest. However, contrary to previous conjectures, here we show clear evidence of bulk magnetic ordering in this compound below $T_N=15$,K by combining bulk magnetization and heat capacity measurements, and local-probe muon spin relaxation measurements. The magnetic ordering in this material is rather unconventional in several respects. Firstly, a crossover regime where the ordered state coexists with the paramagnetic state extends down to $T_N/3$ and, secondly, the fluctuation crossover is shifted far below $T_N$. Moreover, a reduced magnetic-entropy release at $T_N$ and persistent spin dynamics that is observed at temperatures as low as $T/T_N=1/300$ could be a sign of emergent excitations of correlated spin-loops or, alternatively, a sign of fragmentation of each magnetic moment into an ordered and a fluctuating part.
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