Information lattice approach to the metal-insulator transition

TL;DR

This paper demonstrates that the information lattice provides an observable-independent method to analyze the metal-insulator transition in quantum lattice models, revealing distinct scaling behaviors in different regimes.

Contribution

It introduces the application of the information lattice to distinguish metallic and insulating phases without relying on specific observables.

Findings

Information per scale follows a power law in metals at low temperature.

Friedel-like oscillations are visible in the information lattice.

Information per scale decays exponentially in insulators or at high temperature.

Abstract

Correlation functions and correlation lengths are frequently used to describe phase transitions in quantum systems, but they require an explicit choice of observables. The recently introduced information lattice instead provides an observable-independent way to identify where and at which scale information is contained in quantum lattice models. Here, we use it to study the difference between the metallic and insulating regime of one-dimensional noninteracting tight-binding chains. We find that the information per scale follows a power law in metals at low temperature and that Friedel-like oscillations are visible in the information lattice. At high temperature or in insulators at low temperature, the information per scale decays exponentially. Thus, the information lattice is a useful tool for analyzing the metal-insulator transition.