The Fermi liquid theory is a fundamental concept in Condensed Matter Physics (CMP) that describes the behaviour of interacting fermions, particularly conduction electrons in metals at low temperatures.

Developed by Lev Landau in 1956, the theory explains why some properties of an interacting fermion system resemble those of a non-interacting Fermi gas, while others differ.

Identical fermions cannot occupy the same quantum state at the same time. Bosons, however, can share quantum states. But to observe this fundamental difference, gases of bosons or fermions have to be chilled to ultra-low temperatures, where individual quantum states have a high chance of being occupied.

At these low temperatures, bosons will eagerly fall into a single quantum state to form a Bose-Einstein condensate, whereas fermions tend to fill energy states from the lowest up, with one particle per quantum state. At high temperatures, in contrast, bosons and fermions spread out over many states with, on average, much less than one atom per state.

The key idea is that even when electrons interact strongly, their collective behaviour can still be understood in terms of quasiparticles – entities that behave like free electrons, but with modified properties such as effective mass.

The Landau-Fermi Theory provides a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures.

Fermi liquid theory applies to various systems, including:

A crucial aspect of the theory is adiabaticity, meaning that if interactions are introduced gradually, the system’s ground state transforms smoothly without abrupt changes. This allows physicists to study complex many-body systems using relatively simple approximations.

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