We study a single quasihole excitation in a quantum antiferromagnet using a variational wave function that includes spin-spin as well as spin-hole correlations. The wave function can be cast in the form of a complex correlation operator acting on a Marshall-type wave function for the spin background. Such a correlation operator, featuring momentum-dependent spin-hole correlations, is shown to correspond to a coherent local rotation of the spins, which can be also interpreted as a ``spin-backflow'' current, analogous to the Feynman-Cohen backflow current in helium liquids. The variational Monte Carlo method is used to calculate the hole excitation spectrum on a square lattice for the t-J model with this wave function. Comparing our results with available exact results on a 4\ifmmode\times\else\texttimes\fi{}4 square lattice, we find qualitative and semiquantitative agreement. We provide results obtained on much larger lattices. We find that the quasihole energy band attains its minimum at k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) while the hole mass is strongly anisotropic in different directions of k space. The quasihole excitation creates both a planar long-range distortion of the antiferromagnetic (AF) moment of the background \ensuremath{\delta}${\mathit{m}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$(r\ensuremath{\rightarrow}\ensuremath{\infty})\ensuremath{\sim}(k\ensuremath{\cdot}r)/
r2 and a ferromagnetic moment localized in the immediate neighborhood of the hole, pointing in the perpendicular direction. The magnitude of the ferromagnetic moment depends on the momentum of the excitation, and at the minimum of the hole band only the long-range AF planar distortion is present.
Dilution effects on spin-1/2 quantum Heisenberg antiferromagnets with a non-magnetic spin-gapped ground state are studied by means of the quantum Monte Carlo simulation. In the site-diluted system, an antiferromagnetic long-range order (AF-LRO) is induced at an infinitesimal concentration of dilution due to an effective coupling ̃Jmn between induced magnetic moments. In the bond-diluted case, on the other hand, the AF-LRO is not induced up to a certain concentration of dilution due to singlet pairs reformed by an AF coupling ̃J af between the edge spins of the diluted bond through the two-dimensional shortest paths. The competition between ̃Jmn and ̃J af yields peculiar phenomena in the bond-diluted system.
We discuss the effects of nonmagnetic impurities (static holes) in the
S=1/2 Heisenberg model on a two-dimensional (2D) square lattice, and on two- and three-leg ladders. Results of quantum Monte Carlo simulations show that a free localized moment is induced around an isolated impurity only in the spin-gapped two-leg ladder, in agreement with previous theoretical expectations. The localization length of the
S=1/2 impurity moment in a two-leg ladder with isotropic couplings is $\ensuremath{\approx}1.5$ lattice spacings. In gapless ladders (odd number of legs) and in the 2D lattice, no free moments are induced. However, in the 2D system, which has antiferromagnetic long-range order at
T=0 and a gap for longitudinal fluctuations, the impurity leads to a localized distortion of the magnetization in the direction of the broken symmetry, with total
Sz=1/2. The shape of the distortion is in close agreement with previous spin-wave calculations. For all the systems, a staggered moment is induced by the impurity. For the gapped two-leg ladder this is exponentially localized within a length equal to the spin correlation length of the ladder ($\ensuremath{\approx}3.2$ lattice spacings). For the three-leg ladder, the integrated staggered moment diverges as the system size goes to infinity, but the staggered magnetization at a given site appears to vanish. In 2D, we discuss the behavior seen in finite systems both with and without additional symmetry-breaking mechanisms. We also discuss the effect of impurities on the NMR Knight shift and the bulk magnetic susceptibility.
We discuss the universal theory of localized impurities in the paramagnetic state of 2D antiferromagnets where the spin gap is assumed to be significantly smaller than a typical exchange energy. We study the impurity spin susceptibility near the host quantum transition from a gapped paramagnet to a Néel state, and we compute the impurity-induced damping of the spin-1 mode of the gapped antiferromagnet. Under suitable conditions our results apply also to d-wave superconductors. Doped antiferromagnets (AF) have been the subject of intense studies in the context of the cuprate high-temperature superconductors and other layered transition metal compounds. We present a quantum theory of a particular class of doped AF where it is possible to neglect the coupling between the spin and charge degrees of freedom and consider a theory of the spin excitations alone. Such a theory will apply to (i) quasi-2D ‘spin gap ’ insulators like SrCu2O3 or NaV2O5 in
A semiclassical analysis, as well as symmetry considerations, are used to explain and extend published quantum-cluster results for the ground state of a hole in a quantum antiferromagnet (AF). For the ground state with a wave vector in the face center of the reduced Brillouin zone, the spins twist into a dipolar configuration around the hole to optimize the hopping term, but remain coplanar. More complicated three-dimensional spin textures with staggered topological charge can be constructed by superimposing dipole states corresponding to distinct points in the Brillouin zone and different planes of spin twist. An effective Hamiltonian for the hole that generalizes the nonlinear sigma model is derived. The essential new term that is responsible for the textures described is a coupling between spin currents for the holes and background spins. The presence of the local antiferromagnetic correlations dictates a spinor representation of the vacancy. This description provides the foundation for the study of the phases of a quantum AF at low vacancy density.