Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures. The theory describes the behavior of many-body systems of particles in which the interactions between particles may be strong. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal Fermi gas (collection of non-interacting fermions), and why other properties differ.

Fermi liquid theory applies most notably to conduction electrons in normal (non-superconducting) metals, and to liquid helium-3. Liquid helium-3 is a Fermi liquid at low temperatures (but not low enough to be in its superfluid phase). An atom of helium-3 has two protons, one neutron and two electrons, giving an odd number of fermions, so the atom itself is a fermion. Fermi liquid theory also describes the low-temperature behavior of electrons in heavy fermion materials, which are metallic rare-earth alloys having partially filled f orbitals. The effective mass of electrons in these materials is much larger than the free-electron mass because of interactions with other electrons, so these systems are known as heavy Fermi liquids. Strontium ruthenate displays some key properties of Fermi liquids, despite being a strongly correlated material that is similar to high temperature superconductors such as the cuprates. The low-momentum interactions of nucleons (protons and neutrons) in atomic nuclei are also described by Fermi liquid theory.

The key ideas behind Landau's theory are the notion of adiabaticity and the Pauli exclusion principle. Consider a non-interacting fermion system (a Fermi gas), and suppose we "turn on" the interaction slowly. Landau argued that in this situation, the ground state of the Fermi gas would adiabatically transform into the ground state of the interacting system.

By Pauli's exclusion principle, the ground state ${\displaystyle \Psi _{0}}$ of a Fermi gas consists of fermions occupying all momentum states corresponding to momentum ${\displaystyle p<p_{\rm {F}}}$ with all higher momentum states unoccupied. As the interaction is turned on, the spin, charge and momentum of the fermions corresponding to the occupied states remain unchanged, while their dynamical properties, such as their mass, magnetic moment etc. are renormalized to new values. Thus, there is a one-to-one correspondence between the elementary excitations of a Fermi gas system and a Fermi liquid system. In the context of Fermi liquids, these excitations are called "quasiparticles".

Landau quasiparticles are long-lived excitations with a lifetime ${\displaystyle \tau }$ that satisfies ${\displaystyle {\hbar }/{\tau }\ll \varepsilon _{\rm {p}}}$ where ${\displaystyle \varepsilon _{\rm {p}}}$ is the quasiparticle energy (measured from the Fermi energy). At finite temperature, ${\displaystyle \varepsilon _{\rm {p}}}$ is on the order of the thermal energy ${\displaystyle k_{\rm {B}}T}$, and the condition for Landau quasiparticles can be reformulated as ${\displaystyle {\hbar }/{\tau }\ll k_{\rm {B}}T}$.

For this system, the many-body Green's function can be written (near its poles) in the form

where ${\displaystyle \mu }$ is the chemical potential, ${\displaystyle \varepsilon (\mathbf {p} )}$ is the energy corresponding to the given momentum state and ${\displaystyle Z>0}$ is called the quasiparticle residue or renormalisation constant which is very characteristic of Fermi liquid theory. The spectral function for the system can be directly observed via angle-resolved photoemission spectroscopy (ARPES), and can be written (in the limit of low-lying excitations) in the form:

where ${\displaystyle v_{\rm {F}}}$ is the Fermi velocity.