A continuous unitary transformation is introduced which realizes Landau's mapping of the elementary excitations (quasiparticles) of an interacting Fermi liquid system to those of the system without interaction. The conservation of the number of quasiparticles is important. The transformation is performed numerically for a one-dimensional system, i.e., the worst case for a Fermi liquid approach. Yet evidence for Luttinger liquid behavior is found. Such an approach may open a route to a unified description of Fermi and Luttinger liquids on all energy scales.A continuous unitary transformation is introduced which realizes Landau's mapping of the elementary excitations (quasiparticles) of an interacting Fermi liquid system to those of the system without interaction. The conservation of the number of quasiparticles is important. The transformation is performed numerically for a one-dimensional system, i.e., the worst case for a Fermi liquid approach. Yet evidence for Luttinger liquid behavior is found. Such an approach may open a route to a unified description of Fermi and Luttinger liquids on all energy scales.

arXiv:cond-mat/0111078Physical Review LettersMar 22, 200214 citations

Dynamics of fermi liquids

Jagdish Prasad Singh

Jun 30, 19830 citations

THE THEORY OF A FERMI LIQUID

Elsevier eBooksJan 1, 196512 citations

Phase fluctuations and Non-Fermi Liquid Properties of 2D Fermi-system with attraction

V. P. Gusynin, В. М. Локтев, R. M. Quick +1 more

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.

Jan 1, 19991 citation

The Theory of a Fermi Liquid

D. ter Haar

Elsevier eBooksJan 1, 19650 citations

How non-Fermi liquids cure their infrared divergences

Jeremías Aguilera Damia, Mario Solís, Gonzalo Torroba

Non-Fermi liquids in $d=2$ spatial dimensions can arise from coupling a Fermi surface to a gapless boson. At finite temperature, however, the perturbative quantum field theory description breaks down due to infrared divergences. These are caused by virtual static bosonic modes and affect both fermionic and bosonic correlators. We show how these divergences are resolved by self-consistent boson and fermion self-energies that resum an infinite class of diagrams and correct the standard Eliashberg equations. Extending a previous approach in $d=3\ensuremath{-}\ensuremath{\epsilon}$ dimensions, we find a new ``thermal non-Fermi liquid'' regime that violates the scaling laws of the zero-temperature fixed point and dominates over a wide range of scales. We conclude that basic properties of quantum phase transitions and quantum-classical crossovers at finite temperature are modified in crucial ways in systems with soft bosonic fluctuations, and we begin a study of some of the phenomenological consequences.Non-Fermi liquids in $d=2$ spatial dimensions can arise from coupling a Fermi surface to a gapless boson. At finite temperature, however, the perturbative quantum field theory description breaks down due to infrared divergences. These are caused by virtual static bosonic modes and affect both fermionic and bosonic correlators. We show how these divergences are resolved by self-consistent boson and fermion self-energies that resum an infinite class of diagrams and correct the standard Eliashberg equations. Extending a previous approach in $d=3\ensuremath{-}\ensuremath{\epsilon}$ dimensions, we find a new ``thermal non-Fermi liquid'' regime that violates the scaling laws of the zero-temperature fixed point and dominates over a wide range of scales. We conclude that basic properties of quantum phase transitions and quantum-classical crossovers at finite temperature are modified in crucial ways in systems with soft bosonic fluctuations, and we begin a study of some of the phenomenological consequences.

arXiv:2004.05181Physical review. B./Physical review. BJul 27, 202034 citations

Non-Fermi liquids in

d=2

spatial dimensions can arise from coupling a Fermi surface to a gapless boson. At finite temperature, however, the perturbative quantum field theory description breaks down due to infrared divergences. These are caused by virtual static bosonic modes and affect both fermionic and bosonic correlators. We show how these divergences are resolved by self-consistent boson and fermion self-energies that resum an infinite class of diagrams and correct the standard Eliashberg equations. Extending a previous approach in $d=3\ensuremath{-}\ensuremath{\epsilon}$ dimensions, we find a new ``thermal non-Fermi liquid'' regime that violates the scaling laws of the zero-temperature fixed point and dominates over a wide range of scales. We conclude that basic properties of quantum phase transitions and quantum-classical crossovers at finite temperature are modified in crucial ways in systems with soft bosonic fluctuations, and we begin a study of some of the phenomenological consequences.