Dynamical properties of the single--hole $t$--$J$ model on a 32--site square lattice

TL;DR

This study uses exact diagonalization to analyze the spectral function of a single hole in the $t$--$J$ model on a 32-site lattice, revealing dispersion characteristics and spectral features consistent with theoretical predictions and experimental ARPES data.

Contribution

First exact diagonalization analysis of the spectral function for a single hole in the $t$--$J$ model on a 32-site lattice, providing detailed dispersion and spectral weight insights.

Findings

Minimum energy at ${f k} = ({rac{ extpi}{2}}, {rac{ extpi}{2}})$

Spectral dispersion agrees with self--consistent Born approximation

No evidence of string resonances in spectra

Abstract

We present results of an exact diagonalization calculation of the spectral function $A(\bf k, \omega)$ for a single hole described by the $t$--$J$ model propagating on a 32--site square cluster. The minimum energy state is found at a crystal momentum ${\bf k} = ({\pi\over 2}, {\pi\over 2})$, consistent with theory, and our measured dispersion relation agrees well with that determined using the self--consistent Born approximation. In contrast to smaller cluster studies, our spectra show no evidence of string resonances. We also make a qualitative comparison of the variation of the spectral weight in various regions of the first Brillouin zone with recent ARPES data.