Zero-frequency divergence and the gauge phase factor in optical response theory

Static current-current correlation leads to a zero-frequency divergence (ZF D) in the definition of optical susceptibilities. Previous computations hav e shown non-equivalent results for two gauges (p . A and E . r) for exactly the same unperturbed wavefunctions. We reveal that these problems are caus ed by the incorrect treatment of the time-dependent gauge phase factor in o ptical response theory. The gauge phase factor, which is conventionally ign ored by the theory, is important in resolving the ZFD problem and obtaining equivalent results for these two gauges. The Hamiltonians with these two g auges are not necessarily equivalent unless the gauge phase factor is prope rly considered in the wavefunctions. Both Su-Shrieffer-Heeger (SSH) and Tak ayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene serve as illustrativ e examples in studying the linear susceptibility chi((1)) through both curr ent-current and dipole-dipole correlations. Previous improper results of ch i ((1))-calculations and for distribution functions obtained with both gaug es are discussed. The importance of the gauge phase factor in solving the Z FD problem is emphasized on the basis of the SSH and TLM models. As a concl usion, the reason for dipole-dipole correlation being preferable to current -current correlation in practical computations is explained.