We perform a Gutzwiller projected-wave-function study for the spin-1/2 Heisenberg model on the Kagomé lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization. We show that such a U(1)-Dirac state represents a quantum phase whose low-energy physics is governed by four flavors of two-component Dirac fermions coupled to a U(1) gauge field. These results are discussed in the context of recent experiments on ZnCu(3)(OH)(6)Cl(2).
We find that the best resonating valence bond (RVB) state of the spin-
21 kagome antiferromagnetic Heisenberg model (spin-
21 KAFH) is described by a
Z2 mean field ansatz belonging to the ${Z}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ class, which hosts a mean field spinon dispersion very different from that of the widely studied
U(1) Dirac spin liquid state. However, we find that the physical spin fluctuation spectrum calculated from the Gutzwiller projected random phase approximation (RPA) (GRPA) theory above such an RVB state is actually gapless and is almost identical to that above the
U(1) Dirac spin liquid state. We find that such a peculiar behavior can be attributed to the unique flat band physics on the kagome lattice, which makes the mapping between the mean field ansatz and the RVB state noninjective. We find that the spin fluctuation spectrum of the spin-
21 KAFH is not at all featureless, but is characterized by a prominent spectral peak at about
0.25J around the
M point, which is immersed in a broad continuum extending to
2.7J. Based on these results, we argue that the spectral peak below 2 meV in the inelastic neutron scattering spectrum of hebertsmithite
ZnCu3(OH)6Cl2, which has been attributed to the contribution of
Cu2+ impurity spins occupying the
Zn2+ site, should rather be understood as the intrinsic contribution from the kagome layer. We propose to verify such a picture by measuring the Knight shift on the Cu site, rather than the O site, which is almost blind to the spin fluctuation at the
M point as a result of the strong antiferromagnetic correlation between nearest neighboring spins on the kagome lattice.
In recent work, we argued that a particular algebraic spin liquid (ASL) may be the ground state of the
S=1/2 kagome lattice Heisenberg antiferromagnet. Furthermore, this state, which lacks a spin gap, is appealing in light of recent experiments on herbertsmithite
[ZnCu3(OH)6Cl2]. Here, we study the properties of this ASL in more detail using both the low-energy effective field theory and Gutzwiller-projected wave functions of fermionic spinons. We identify the competing orders of the ASL, which are observables having slowly decaying power-law correlations---among them we find a set of magnetic orders lying at the
M points of the Brillouin zone, the familiar $\mathbit{q}=0$ magnetic ordered state, the ``Hastings'' valence-bond solid (VBS) state, and a pattern of vector spin-chirality ordering corresponding to one of the Dzyaloshinskii--Moriya (DM) interaction terms present in herbertsmithite. Identification of some of these orders requires an understanding of the quantum numbers of magnetic monopole operators in the ASL. We discuss the detection of the magnetic and VBS competing orders in experiments. While we primarily focus on a clean system without DM interaction, we consider the effects of small DM interaction and argue that, surprisingly, it leads to spontaneously broken time-reversal symmetry (for DM interaction that preserves
XY spin rotation symmetry, there is also
XY magnetic order). Our analysis of the projected wave function provides an estimate of the ``Fermi velocity''
vF that characterizes all low-energy excitations of the ASL---this allows us to estimate the specific heat, which compares favorably with experiments. We also study the spin and bond correlations of the projected wave function and compare these results with those of the effective field theory. While the spin correlations in the effective field theory and wave function seem to match rather well (although not completely), the bond correlations are more puzzling. We conclude with a discussion of experiments in herbertsmithite and make several predictions.