On the spectral function of a hole in a one-dimensional quantum antiferromagnet

Satyaki Kar, Efstratios Manousakis

Q. F. Zhong, Sandro Sorella, Alberto Parola

The one-hole spectral weight for two chains and two-dimensional lattices is studied numerically using a method of analysis of the spectral function within the Lanczos iteration scheme: the Lanczos spectral decoding method. This technique is applied to the t-${\mathit{J}}_{\mathit{z}}$ model for ${\mathit{J}}_{\mathit{z}}$\ensuremath{\rightarrow}0, directly on an infinite-size lattice. By a careful investigation of the first 13 Lanczos steps and the first 26 ones for the two-dimensional and the two-chain cases, respectively, we find several interesting features of the one-hole spectral weight. A sharp incoherent peak with a clear momentum dispersion is identified, together with a second broad peak at higher energy. The spectral weight is finite up to the Nagaoka energy where it vanishes in a nonanalytic way. Thus the lowest energy of one hole in a quantum antiferromagnet is degenerate with the Nagaoka energy in the thermodynamic limit.

A. Sherman

Weijie Zhang, Jue-lian Shen

We have studied one-hole dynamics in a quantum antiferromagnet by use of the anisotropic three-dimensional t-J model in the simple cubic lattice within the self-consistent Born approximation. The hole spectral function, the density of states, the quasiparticle dispersion relationship, the effective mass, the quasiparticle spectral weight, and the incoherent multiple spin-wave background are determined as functions of the Heisenberg exchange and hopping amplitude in the thermodynamic limit.

Zhao-Bin Su, Yan-min Ll, W. Y. Lai +1 more

Weijie Zhang, Jue-lian Shen

We have investigated one-hole motion in the anisotropic three-dimensional (A3D) quantum antiferromagnet by use of the A3D t-J model in a simple cubic lattice. The hopping matrix element and the Heisenberg exchange energy are t and J in the xy plane. They are ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ in the z direction. Within the self-consistent mean-field approximation, the hole spectral function has been calculated by use of an iterative technique. We find that the quasiparticle picture still holds and the lowest-energy quasiparticle state has momentum either k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2,\ensuremath{\pi}/2) or k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2,0) depending on the parameters of the model. Holding J and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ constant and allowing ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ to increase, the spectral weight and the peak height of the quasiparticle decreases. In the quasi-two-dimensional cases with small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, the spectral weight and the peak height of the quasiparticle are smaller than those in the exact two-dimensional case.