Luttingerliquid

A Luttinger liquid is a theoretical model in condensed matter physics that describes the low-energy behavior of interacting one-dimensional electrons. In one dimension, electron-electron interactions cannot be ignored and significantly alter the properties of the system compared to the non-interacting Fermi liquid model, which is typically valid in higher dimensions. The key feature of the Luttinger liquid is that the elementary excitations are not individual electrons but rather collective density or spin waves, often referred to as "bosons." These excitations have a linear dispersion relation at low energies and momenta, a characteristic that distinguishes them from the quasiparticles of a Fermi liquid.

The theory of Luttinger liquids, developed by Joaquin Mazdak Luttinger, demonstrates that in one dimension, the correlation functions of interacting electrons decay as a power law, rather than exponentially as in a Fermi liquid. This power-law behavior leads to unusual physical properties, such as a vanishing density of states at the Fermi level and the absence of well-defined quasiparticles. Experimental realizations of Luttinger liquid behavior are found in various one-dimensional systems, including quantum wires, organic conductors, and carbon nanotubes. Understanding Luttinger liquids is crucial for comprehending the exotic phenomena observed in these low-dimensional electronic systems.