Optical conductivity of strongly correlated electron systems

TL;DR

This study uses exact diagonalization to analyze the optical conductivity in small 2D t-J model clusters, revealing resonance features linked to spin-bag excitations and the dominant energy scale of the system.

Contribution

It provides a detailed numerical analysis of the frequency and wave vector dependent conductivity in the 2D t-J model, highlighting the role of exchange interactions and quasiparticle excitations.

Findings

Resonance at ~1.7J in underdoped regime

t remains the main energy scale at higher doping levels

String picture explains numerical results semi-quantitatively

Abstract

We present an exact diagonalization study of the frequency and wave vector dependent conductivity $\sigma(q,\omega)$ in small clusters of $2D$ $t$$-$$J$ model. Unlike the related dynamical density correlation function, $\sigma(q=0,\omega)$ in the underdoped regime has the exchange constant $J$ as its characteristic energy scale and is dominated by a resonance-like excitation with frequency $\sim 1.7J$. We interpret this as transition to a $p$-like excited state of a spin-bag type quasiparticle (or, alternatively, a tightly bound spinon-holon pair) and show that a simple calculation based on the string picture explains the numerical results semiquantitatively. For doping levels $\ge 25% t$ remains the only energy scale of $\sigma(q=0,\omega)$.