A measure of localization properties of one-dimensional single electron lattice systems

• A novel quantity is proposed to measure the degree of localization.
• It includes information about the spatial variation of probability density.
• It is a fruitful index to monitor the localization–delocalization transition.

We propose a novel quantity to measure the degree of localization properties of various types of one-dimension single electron states. The quantity includes information about the spatial variation of probability density of quantum states. Numerical results show that it can distinguish localized states from delocalized ones, so it can be used as a fruitful index to monitor the localization–delocalization transition. Comparing with existing measures, such as geometric average density of states, inverse participation ratio, and quantum information entropies, our proposed quantity has some advantages over them.