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Register a new userGapless spin liquid in the kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
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A preponderance of evidence suggests that the ground state of the nearest-neighbor $S = 1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, $D_c/J simeq 0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need to reassess the apparent spin-liquid behavior reported in this system.
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The nature of the ground state of the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings $J_{vartriangle}$ and $J_{triangledown}$ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped $mathbb{Z}_{2}$ spin liquid. For several values of the ratio $J_{triangledown}/J_{vartriangle}$, the size scaling of the energy gain due to the pairing fields and the variational parameters are reported. Our results show that the energy gain of the gapped spin liquid with respect to the gapless state either vanishes for large enough system size or scales to zero in the thermodynamic limit. Similarly, the optimized pairing amplitudes (responsible for opening the spin gap) are shown to vanish in the thermodynamic limit. Our outcome is corroborated by the application of one and two Lanczos steps to the gapless and gapped wave functions, for which no energy gain of the gapped state is detected when improving the quality of the variational states. Finally, we discuss the competition with the simplex $mathbb{Z}_{2}$ resonating-valence-bond spin liquid, valence-bond crystal, and nematic states in the strongly anisotropic regime, i.e., $J_{triangledown} ll J_{vartriangle}$.
The $S$ = $frac{1}{2}$ kagome Heisenberg antiferromagnet (KHA) is a leading model hosting a quantum spin liquid (QSL), but the exact nature of its ground state remains a key issue under debate. In the previously well-studied candidate materials, magnetic defects always dominate the low-energy spectrum and hinder the detection of the intrinsic nature. We demonstrate that the new single crystal of YCu$_3$[OH(D)]$_{6.5}$Br$_{2.5}$ is a perfect KHA without evident magnetic defects ($ll$ 0.8%). Through fitting the magnetic susceptibilities of the orientated single crystals, we find the spin system with weak anisotropic interactions and with first-, second-, and third-neighbor couplings, $J_1$ $sim$ 56 K and $J_2$ $sim$ $J_3$ $sim$ 0.1$J_1$, belongs to the continuous family of fully frustrated KHAs. No conventional freezing is observed down to 0.36 K $sim$ 0.006$J_1$, and the raw specific heat exhibits a nearly quadratic temperature dependence below 1 K $sim$ 0.02$J_1$, well consistent with a gapless (spin gap $leq$ 0.025$J_1$) Dirac QSL.
The quantum spin liquid material herbertsmithite is described by an antiferromagnetic Heisenberg model on the kagome lattice with non-negligible Dzyaloshinskii-Moriya interaction~(DMI). A well established phase transition to the $mathbf q=0$ long-range order occurs in this model when the DMI strength increases, but the precise nature of a small-DMI phase remains controversial. Here, we describe a new phase obtained from Schwinger-boson mean-field theory that is stable at small DMI, and which can explain the dispersionless spectrum seen in inelastic neutron scattering experiment by Han et al (Nature (London) 492, 406 (2012)}). It is a time-reversal symmetry breaking $mathbb Z_2$ spin liquid, with the unique property of a small and constant spin gap in an extended region of the Brillouin zone. The phase diagram as a function of DMI and spin size is given, and dynamical spin structure factors are presented.
Motivated by recent experiments on the Heisenberg S=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 anti-ferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.
We investigate the spin-1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e. with weak and strong triangular units), constructing an improved simplex Resonating Valence Bond (RVB) ansatz by successive applications (up to three times) of local quantum gates which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting Projected Entangled Pair State involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB provides very good variational energies at strong and even intermediate breathing anisotropy. We show that it carries $Z_2$ topological order which does not fade away under the first few applications of the quantum gates, suggesting that the RVB topological spin liquid becomes a competing ground state candidate for the kagome antiferromagnet at large breathing anisotropy.
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