Dynamical Properties of a Single Hole in an Antiferromagnet

TL;DR

This study investigates the spectral and optical properties of a single hole in an antiferromagnetic background using finite size scaling, revealing robust quasiparticle features and large effective masses, with implications for understanding hole dynamics in correlated materials.

Contribution

It provides a detailed finite size scaling analysis of spectral functions and optical conductivity, demonstrating the robustness of quasiparticle peaks and clarifying the effects of spin fluctuations and system size.

Findings

Quasiparticle peaks are robust across increasing cluster sizes.

The hole's optical mass exceeds 20, indicating heavy quasiparticles.

A small gap separates low energy states, disappearing with spin fluctuations.

Abstract

A finite size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low energy quasiparticle peak and the broad higher energy structure are robust with increasing cluster size from $4\times 4$ to $\sqrt{26}\times\sqrt{26}$ sites. In the abscence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size $N_c(J_z)$. Typically, 16 and 26 site clusters give reliable results for $J_z>0.75$ and $J_z>0.3$ respectively. The hole optical mass is shown to be very large ($>20$) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap $\propto J_z$ separates the low energy delta-function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with $J_\perp$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation. An accurate estimation of the higher energy part of the spectral functions of the t--J model can be made for momenta close to $(0,0)$ or $(\pi,\pi)$;