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Physical review. B, Condensed matter

Ground state of a mobile vacancy in a quantum antiferromagnet: Small-cluster study

Veit Elser, David A. Huse, Boris I. Shraiman, Eric D. Siggia

Published Apr 1, 1990• 77 citations
Publisher

Abstract

The ground state of a mobile vacancy in a square-lattice spin-1/2 Heisenberg antiferromagnet described by the t-J Hamiltonian is investigated numerically for an 18-site cluster. The ground state has spin 1/2, and the bottom of the vacancy band is at momentum k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), for t/J4, which is consistent with the spin-wave perturbation theory. The structure of the spin configuration in the vicinity of the vacancy is examined using a number of correlation functions. The latter reveal the existence of a dipolar distortion of the staggered magnetization, as suggested by the semiclassical theory.

DOI
10.1103/physrevb.41.6715

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Physical review. B, Condensed matter•Sep 1, 1990•35 citations
The ground state of a mobile vacancy in a square-lattice spin-1/2 Heisenberg antiferromagnet described by the t-J Hamiltonian is investigated numerically for an 18-site cluster. The ground state has spin 1/2, and the bottom of the vacancy band is at momentum k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), for t/J4, which is consistent with the spin-wave perturbation theory. The structure of the spin configuration in the vicinity of the vacancy is examined using a number of correlation functions. The latter reveal the existence of a dipolar distortion of the staggered magnetization, as suggested by the semiclassical theory.
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.
The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice is studied by the numerical-diagonalization method. This lattice is obtained by the combination of the Lieb lattice and the square lattice. It is known that when interaction on the square lattice is increased from the ferrimagnetic limit of strong interaction on the Lieb lattice, this system shows gradual decrease and disappearance of spontaneous magnetization in the ground state. The present study treats the region near the case of the square-lattice antiferromagnet accompanied by isolated spins by numerical-diagonalization calculations of finite-size clusters with the maximum size of 39 sites. Our numerical results suggest the existence of a new phase with small but nonzero spontaneous magnetization between two zero-spontaneous-magnetization phases.
The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice is studied by the numerical-diagonalization method. This lattice is obtained by the combination of the Lieb lattice and the square lattice. It is known that when interaction on the square lattice is increased from the ferrimagnetic limit of strong interaction on the Lieb lattice, this system shows gradual decrease and disappearance of spontaneous magnetization in the ground state. The present study treats the region near the case of the square-lattice antiferromagnet accompanied by isolated spins by numerical-diagonalization calculations of finite-size clusters with the maximum size of 39 sites. Our numerical results suggest the existence of a new phase with small but nonzero spontaneous magnetization between two zero-spontaneous-magnetization phases.
We have studied hole states on square lattices with 8, 10, 16, 18, and 20 sites by exactly diagonalizing the single-hole t-J model with twisted boundary conditions in the whole Brillouin zone. The bottom of the hole band is found to be extremely flat and anisotropic. The hole effective mass is highly anisotropic and enhanced in a quantum antiferromagnet. The momentum of a hole in the ground state is not located at high-symmetry points such as (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0), or (0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}). They are strongly lattice-size dependent and weakly parameter J/t (t is the hopping constant and J is the exchange constant) dependent. As the lattice size increases, the momentum of the ground state approaches the zone face center (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).
Th t-t'-t''-J model is investigated by a rigorous diagonalization in a two-dimensional square lattice as large as \ensuremath{\surd}20 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}20 , which has no additional degeneracy. The ground state of one hole in the t-J model is at a momentum k near (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) with a total spin S=1/2 and that of two holes is at k=(0,0) with S=0. The hole pairing and nonclustering may be preferable for the ground state of the t-t'-t''-J model in the region of t'>0 and t''\ensuremath{\lesssim}0.