Charge dynamics of t-J model and anomalous bond-stretching phonons in cuprates

TL;DR

This paper investigates the charge dynamics in the t-J model of cuprates, revealing how polaron effects influence phonon behavior and align with experimental observations of phonon anomalies.

Contribution

It introduces a 1/N slave boson approach to accurately describe charge fluctuations and phonon anomalies in doped cuprates, improving upon previous models.

Findings

Identifies a broad dispersive peak in density response spectra consistent with numerical studies.

Reveals a low energy feature related to polaron motion in the spinon background.

Explains the anomalous damping of bond-stretching phonons in La$_{2-x}$Sr$_x$CuO$_4$.

Abstract

The density response of a doped Mott-Hubbard insulator is discussed starting from the t-J model in a slave boson 1/N representation. In leading order O(1) the density fluctuation spectra $N({\bf q},\omega)$ are determined by an undamped collective mode at large momentum transfer, in striking disagreement with results obtained by exact diagonalization, which reveal a very broad dispersive peak, reminescent of strong spin-charge coupling. The 1/N corrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resulting $N({\bf q},\omega)$ captures all features observed in diagonalization studies, fulfills the appropriate sum rules, and apart from the broadening of the collective mode shows a new low energy feature at the energy $\chi J+\delta t$ related to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in $(\pi,0)$ direction, describes the strong renormalization and anomalous damping of the highest bond-stretching phonons in La$_{2-x}$Sr$_x$CuO$_4$.