What is Tomonaga-Luttinger liquid theory?
The Tomonaga–Luttinger liquid theory describes the behavior of interacting electrons in one-dimensional systems. It is natural to think that electrons in a wire would behave like a Fermi liquid, but in one dimension, quantum fluctuations become so strong that the usual quasiparticle picture breaks down. Instead, the collective excitations—charge and spin waves—separate and propagate at different velocities. I first proposed this model in 1950, and later Joaquin Luttinger extended it. The essential point is that this theory predicts phenomena like spin-charge separation, which has been observed in carbon nanotubes and quantum wires. We must be careful not to confuse the mathematics with the physics: the beauty lies in how simple interactions lead to such rich behavior. It remains a cornerstone for understanding low-dimensional systems today.
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