Hole dynamics in thet-Jmodel: An exact diagonalization study

Abstract

Exact many-body states of square clusters up to 18 sites (with periodic boundary conditions) are investigated in order to study the dynamics of one or two holes in the t-J model. Our method takes full advantage of the translation, rotation, and reflection symmetries of the cluster. Using a modified Lanczos algorithm, we calculate the lowest state of all the different space-group representations and its total spin as well as its spin and hole correlations. For a single hole, at intermediate J/t values, the magnetic, kinetic energies, and staggered magnetization follow J/t power-law behaviors with size-dependent exponents. A binding energy of order J between two holes appears for sufficiently large J/t(≥0.25). One-hole and two-hole calculations give different results regarding the stability of the Nagaoka state (against the singlet state) when J/t→0. Energy expectation values of variational resonating-valence-bond states are calculated exactly and optimized. Significant overlaps with the exact states are found for any symmetry.