We study the Gutzwiller ansatz with a gauge field and aribtrary polarization as a trial wave function for the spin-liquid state of the Heisenberg Hamiltonian in two dimensions. This wave function is evaluated exactly for a 4\ifmmode\times\else\texttimes\fi{}4 cluster with periodic boundary conditions. The energy as a function of the gauge field and magnetization is calculated.
We study the Gutzwiller ansatz with a gauge field and aribtrary polarization as a trial wave function for the spin-liquid state of the Heisenberg Hamiltonian in two dimensions. This wave function is evaluated exactly for a 4\ifmmode\times\else\texttimes\fi{}4 cluster with periodic boundary conditions. The energy as a function of the gauge field and magnetization is calculated.
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).
Understanding the nature of the excitation spectrum in quantum spin liquids is of fundamental importance, in particular for the experimental detection of candidate materials.However, current theoretical and numerical techniques have limited capabilities, especially in obtaining the dynamical structure factor, which gives a crucial characterization of the ultimate nature of the quantum state and may be directly assessed by inelastic neutron scattering.In this work, we investigate the low-energy properties of the S ¼ 1=2 Heisenberg model on the triangular lattice, including both nearest-neighbor J 1 and next-nearestneighbor J 2 superexchanges, by a dynamical variational Monte Carlo approach that allows accurate results on spin models.For J 2 ¼ 0, our calculations are compatible with the existence of a well-defined magnon in the whole Brillouin zone, with gapless excitations at K points (i.e., at the corners of the Brillouin zone).The strong renormalization of the magnon branch (also including rotonlike minima around the M points, i.e., midpoints of the border zone) is described by our Gutzwiller-projected state, where Abrikosov fermions are subject to a nontrivial magnetic π flux threading half of the triangular plaquettes.When increasing the frustrating ratio J 2 =J 1 , we detect a progressive softening of the magnon branch at M, which eventually becomes gapless within the spin-liquid phase.This feature is captured by the band structure of the unprojected wave function (with two Dirac points for each spin component).In addition, we observe an intense signal at low energies around the K points, which cannot be understood within the unprojected picture and emerges only when the Gutzwiller projection is considered, suggesting the relevance of gauge fields for the low-energy physics of spin liquids.
We study Gutzwiller-projected wave functions for triangular-lattice U(1) Dirac spin liquids in a Zeeman field, where we allow the U(1) gauge field to develop a gauge flux, resulting in (spin-split) spinon Landau levels. We find that at a given magnetization, the optimal candidate state has a finite flux chosen such that the spinon filling lies in a |C|=1 Landau-level gap: it gives the lowest variational energy and the smallest energy variance within our correlation-matrix reconstruction for local Heisenberg-type models. By symmetry, we argue that the finite gauge flux results in a nonzero (staggered) scalar spin chirality, as also numerically observed, and further find that the |C|=1 state exhibits dominant quasi-long-ranged 120° magnetic correlations. Studying the next-to-optimal wave function with a |C|=2 Landau-level gap, we observe unusual spin-nematic correlations. Our results may provide guidance for analyzing the magnetic-field response of Dirac spin liquid candidate materials and offer numerical diagnostics that can connect to the underlying theory of spinons coupled to an emergent U(1) gauge field.
The parton approach for quantum spin liquids gives a transparent description of low-energy elementary excitations, e.g., spinons and emergent gauge-field fluctuations. The latter ones are directly coupled to the hopping/pairing of spinons. By using the fermionic representation of the U(1) Dirac state on the kagome lattice and variational Monte Carlo techniques to include the Gutzwiller projection, we analyze the effect of modifying the gauge fields in the spinon kinematics. In particular, we construct low-energy monopole excitations, which are shown to be gapless in the thermodynamic limit. States with a finite number of monopoles or with a finite density of them are also considered, with different patterns of the gauge fluxes. We show that these chiral states are not stabilized in the Heisenberg model with nearest-neighbor superexchange couplings, and the Dirac state corresponds to the lowest-energy ansatz within this family of variational wave functions. Our results support the idea that spinons with a gapless conical spectrum coexist with gapless monopole excitations, even for the spin-1/2 case.
We establish that spin liquids described in terms of gapless fermionic (Dirac) spinons and gapless U(1) gauge fluctuations can be stable in two dimensions, at least when the physical SU(2) spin symmetry is generalized to SU(N). Equivalently, we show that compact QED3 has a deconfined phase for a large number of fermion fields, in the sense that monopole fluctuations can be irrelevant at low energies. A precise characterization is provided by an emergent global topological U(1) symmetry corresponding to the conservation of gauge flux. Beginning with an SU(N) generalization of the S=1∕2 square-lattice Heisenberg antiferromagnet, we consider the $\ensuremath{\pi}$-flux spin liquid and, via a systematic analysis of all operators, show that there are no relevant perturbations (in the renormalization-group sense) about the large-N spin-liquid fixed point, which is thus a stable phase. We provide a further illustration of this conclusion with an approximate renormalization-group calculation that treats the gapless fermions and the monopoles on an equal footing. This approach directly points out some of the flaws in the erroneous ``screening'' argument for the relevance of monopoles in compact QED3.
By using the variational Monte Carlo technique, we study the spin-21 XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice. A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids [with U(1) or Z2 symmetry] or magnetically ordered phases [with q=(0,0) or $\mathbf{q}=(4\ensuremath{\pi}/3,0)$]. We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from U(1) to Z2 within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the U(1) Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing S=2 spin gap is obtained at the variational level, in the whole regime from the XY to the Heisenberg model.