Editing Fermi liquid theory (section)

==Non-Fermi liquids==
'''Non-Fermi liquids''' are systems in which the Fermi-liquid behaviour breaks down. The simplest example is a system of interacting fermions in one dimension, called the [[Luttinger liquid]].<ref name=schulz /> Although Luttinger liquids are physically similar to Fermi liquids, the restriction to one dimension gives rise to several qualitative differences such as the absence of a ''quasiparticle peak'' in the momentum dependent spectral function, and the presence of [[spin-charge separation]] and of [[spin-density wave]]s. One cannot ignore the existence of interactions in one dimension and has to describe the problem with a non-Fermi theory, where Luttinger liquid is one of them. At small finite spin temperatures in one dimension the ground state of the system is described by spin-incoherent Luttinger liquid (SILL).<ref name=soltanieh-ha>{{cite journal|last=M. Soltanieh-ha|first=A. E. Feiguin|title=Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath|year=2012|journal= Physical Review B|volume=86|issue=20|page= 205120 |doi= 10.1103/PhysRevB.86.205120 | arxiv=1211.0982|bibcode = 2012PhRvB..86t5120S |s2cid=118724491}}</ref>

Another example of non-Fermi-liquid behaviour is observed at [[quantum critical point]]s of certain second-order [[phase transition]]s, such as [[heavy fermion]] criticality, [[Mott insulator|Mott criticality]] and high-<math>T_{\rm c}</math> [[High-temperature superconductivity#Cuprates|cuprate]] phase transitions.<ref name=senthil /> The ground state of such transitions is characterized by the presence of a sharp Fermi surface, although there may not be well-defined quasiparticles. That is, on approaching the critical point, it is observed that the quasiparticle residue <math>Z\to0</math>.

In optimally doped cuprates and iron-based superconductors, the normal state above the critical temperature shows signs of non-Fermi liquid behaviour, and is often called a '''strange metal'''. In this region of phase diagram, resistivity increases linearly in temperature and the Hall coefficient is found to depend on temperature.<ref>{{Cite journal |last1=Lee |first1=Patrick A. |last2=Nagaosa |first2=Naoto |last3=Wen |first3=Xiao-Gang |date=2006-01-06 |title=Doping a Mott insulator: Physics of high-temperature superconductivity |url=https://link.aps.org/doi/10.1103/RevModPhys.78.17 |journal=Reviews of Modern Physics |language=en |volume=78 |issue=1 |pages=17–85 |doi=10.1103/RevModPhys.78.17 |issn=0034-6861|arxiv=cond-mat/0410445 |bibcode=2006RvMP...78...17L }}</ref><ref>{{Cite journal |last=Varma |first=Chandra M. |date=2020-07-07 |title=Colloquium : Linear in temperature resistivity and associated mysteries including high temperature superconductivity |url=https://link.aps.org/doi/10.1103/RevModPhys.92.031001 |journal=Reviews of Modern Physics |language=en |volume=92 |issue=3 |page=031001 |doi=10.1103/RevModPhys.92.031001 |issn=0034-6861|arxiv=1908.05686 |bibcode=2020RvMP...92c1001V }}</ref>

Understanding the behaviour of non-Fermi liquids is an important problem in condensed matter physics. Approaches towards explaining these phenomena include the treatment of ''marginal Fermi liquids''; attempts to understand critical points and derive [[critical scaling|scaling relations]]; and descriptions using ''emergent'' [[gauge theory|gauge theories]] with techniques of [[Holographic principle|holographic]] gauge/gravity duality.<ref name=polchinsky>{{cite journal|last=Faulkner|first=Thomas|author2=Polchinski, Joseph|title=Semi-Holographic Fermi Liquids|year=2010| arxiv=1001.5049|doi=10.1007/JHEP06(2011)012|volume=2011|issue=6|pages=12|journal=Journal of High Energy Physics|bibcode=2011JHEP...06..012F|citeseerx=10.1.1.755.3304|s2cid=119243857}}</ref><ref>{{cite journal | last1=Guo | first1=Haoyu | last2=Gu | first2=Yingfei | last3=Sachdev | first3=Subir | title=Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode | journal=Annals of Physics | volume=418 | date=2020 | doi=10.1016/j.aop.2020.168202 | page=168202| arxiv=2004.05182 | bibcode=2020AnPhy.41868202G }}</ref><ref>{{cite journal | last1=Wei | first1=Chenan | last2=Sedrakyan | first2=Tigran A. | title=Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: From flat bands to weakly coupled Sachdev-Ye-Kitaev bundles | journal=Physical Review B | volume=108 | issue=6 | date=2023-08-02 | issn=2469-9950 | doi=10.1103/PhysRevB.108.064202 | page=064202| arxiv=2205.09766 | bibcode=2023PhRvB.108f4202W }}</ref>