Tomonaga–Luttinger model

The Tomonaga–Luttinger model describes how electrons behave in one-dimensional systems, like tiny wires. Unlike in higher dimensions, electrons in these narrow spaces don't act like individual particles; instead, their interactions create collective excitations, similar to waves. This model helps explain phenomena such as unusual electrical conductance and the breakdown of traditional theories, showing that in one dimension, electrons are strongly correlated, leading to unique properties that differ from standard metallic behavior. It’s a fundamental tool for understanding quantum materials confined to very small, one-dimensional structures.