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 compute the dynamical structure factor of the spin-½ triangular Heisenberg model using the mean-field Schwinger boson theory. We find that a reconstructed dispersion, resulting from a non-trivial redistribution of the spectral weight, agrees quite well with the spin excitation spectrum recently found with series expansions. In particular, we recover the strong renormalization with respect to linear spin wave theory along with the appearance of roton-like minima. Furthermore, near the roton-like minima the contribution of the two spinon continuum to the static structure factor is about 40% of the total weight. By computing the density-density dynamical structure factor, we identify an unphysical weak signal of the spin excitation spectrum with the relaxation of the local constraint of the Schwinger bosons at the mean-field level. Based on the accurate description obtained for the static and dynamic ground-state properties, we argue that the bosonic spinon theory should be considered seriously as a valid alternative to interpret the physics of the triangular Heisenberg model.
The Schwinger boson theory provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semiclassical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to further develop this formalism. These points include the freedom for the choice of the saddle point (Hubbard-Stratonovich decoupling and choice of the condensate) and the
1/N expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in
1/N, which must be accounted for to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.
We find that the Schwinger boson mean field theory (SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-12triangular lattice antiferromagnetic Heisenberg model (spin-12TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as a magnon mode. The SBMFT also predicts incorrectly a gapless longitudinal spin fluctuation mode in the magnetic ordered phase. We show that these failures are related to the following facts: (1) spinon condensation fails to provide a consistent description of the order parameter manifold of the 120 degree ordered phase. (2) There lacks in the SBMFT the coupling between the uncondensed spinon and the spinon condensate, which breaks both the spin rotational and the translational symmetry. (3) There lacks in the SBMFT the rigidity that is related to the no double occupancy constraint on the spinon system. We show that such failures of the SBMFT is neither restricted to the spin-12TLHAF nor to the magnetic ordered phase. We proposed a generalized SBMFT to resolve the first two issues and a new formalism to address the third issue.
The dynamical dimer structure factor is an observable probing spin-singlet excitations of quantum magnets distinct from those commonly studied by the spin structure factor. We report the dimer response for the extended spin-
1/2 antiferromagnetic Heisenberg model on the triangular lattice using large-scale GPU-accelerated matrix-product-state simulations. We investigate the ordered phases with
120∘ coplanar, collinear stripe, and tetrahedral spin order, as well as candidate quantum spin-liquid (QSL) regimes, comprising an expected gapless
U(1) Dirac QSL and a chiral QSL at finite spin-scalar-chirality coupling. In the ordered phases, we find low-energy modes below the onset of the two-magnon continuum illustrating avoided quasiparticle decay. Within the candidate gapless QSL, we observe absolute dispersion minima at momenta of half the Brillouin zone corners,
X≡K/2, in agreement with field-theory predictions that singlet monopole excitations of the
U(1) Dirac spin liquid become gapless at these points. Thus, the high-resolution dynamical dimer response provides support for a
U(1) Dirac QSL with singlet monopole excitations.
Dynamical spin structure factors of quantum spin nematic states are calculated in a spin-
21 square-lattice
J1-
J2 model with ferromagnetic
J1 and competing antiferromagnetic
J2 interactions. To this end, we use a fermion representation, generalizing it to
N flavors. We begin with a spin-triplet pairing state of fermion fields, called
Z2 planar state, which is a stable saddle-point solution in the large-
N limit in a finite parameter range where the couplings
J1 and
J2 compete strongly [R. Shindou and T. Momoi, Phys. Rev. B 80, 064410 (2009)]. Using a large-
N expansion, we take into account fluctuations around this saddle point up to corrections of order
1/N. The dynamical spin structure factors thus obtained signify the existence of gapless
q-linear director-wave (spin-wave) modes at $\mathbit{q}=(0,0)$ and gapped ``gauge-field''-like collective modes at $\mathbit{q}=(\ensuremath{\pi},\ensuremath{\pi})$, whose spectral weight vanishes as a linear and quadratic function of the momentum, respectively. The low-energy collective modes contain fluctuations of nematic-director, spin, and gauge degrees of freedom. Associated with the gapless
q-linear modes, we evaluate the temperature dependence of the nuclear spin relaxation rate
1/T1 in the low-temperature regime as $1/{T}_{1}\ensuremath{\propto}{T}^{2d\ensuremath{-}1}$, where
d is the effective spatial dimension.