Singular perturbation theory for interacting fermions in two dimensions

Abstract

We consider a system of interacting fermions in two dimensions beyond the second-order perturbation theory in the interaction. It is shown that the mass-shell singularities in the self-energy, arising already at the second order of the perturbation theory, manifest a non-perturbative effect: an interaction with the zero-sound mode. Resumming the perturbation theory for a weak, short-range interaction and accounting for a finite curvature of the fermion spectrum, we eliminate the singularities and obtain the results for the quasi-particle self-energy and the spectral function to all orders in the interaction with the zero-sound mode. A threshold for emission of zero-sound waves leads a non-monotonic variation of the self-energy with energy (or momentum) near the mass shell. Consequently, the spectral function has a kink-like feature. We also study in detail a non-analytic temperature dependence of the specific heat, $C(T)\propto T^2$. It turns out that although the interaction with the collective mode results in an enhancement of the fermion self-energy, this interaction does not affect the non-analytic term in $C(T)$ due to a subtle cancellation between the contributions from the real and imaginary parts of the self-energy. For a short-range and weak interaction, this implies that the second-order perturbation theory suffices to determine the non-analytic part of $C(T)$. We also obtain a general form of the non-analytic term in $C(T)$, valid for the case of a generic Fermi liquid, \emph{i.e.}, beyond the perturbation theory.

53 pages, 10 figures

References in corpus (1)

• Temperature dependent effective mass renormalization in a Coulomb Fermi liquid

Cited by in corpus (63)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• The effect of collective spin-1 excitations on electronic spectra in high-Tc superconductors
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Skyrmion Crystal from RKKY Interaction Mediated by 2D Electron Gas
• Nuclear Magnetism and Electronic Order in 13C Nanotubes
• Renormalization group analysis of competing orders and the pairing symmetry in Fe-based superconductors
• Fermi liquid near Pomeranchuk quantum criticality
• First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy
• Magnetic Ordering of Nuclear Spins in an Interacting 2D Electron Gas
• Optical response of correlated electron systems
• Strong coupling theory of heavy fermion criticality
• Interaction effects on magnetooscillations in a two-dimensional electron gas
• Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition
• Strongly correlated two-dimensional plasma explored from entropy measurements
• Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid
• Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid
• Spin susceptibility of interacting two-dimensional electrons in the presence of spin-orbit coupling
• Non-analytic spin susceptibility of a nested Fermi liquid: the case of Fe-based pnictides
• Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions
• Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids
• Nonanalytic Magnetic Response of Fermi- and non-Fermi Liquids
• Local Spin Susceptibilities of Low-Dimensional Electron Systems
• Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order
• Spin-liquid insulators can be Landau's Fermi liquids
• Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion
• Berry Fermi Liquid Theory
• Effective Soft-Mode Theory of Strongly Interacting Fermions
• Optical Conductivity of a Two-Dimensional Electron Liquid with Spin-Orbit Interaction
• Free energy and specific heat near a quantum critical point of a metal
• Model of Quantum Criticality in He3 bilayers Adsorbed on graphite
• Luttinger-Ward functional approach in the Eliashberg framework : A systematic derivation of scaling for thermodynamics near a quantum critical point
• Cooper channel and the singularities in the thermodynamics of a Fermi liquid
• Smearing of the 2D Kohn anomaly in a nonquantizing magnetic field: Implications for the interaction effects
• Thermodynamic signatures of an antiferromagnetic quantum critical point inside a superconducting dome
• Momentum dependence of the spin susceptibility in two dimensions: nonanalytic corrections in the Cooper channel
• Nonanalyticities in a Strongly Correlated Fermi Liquid: Corrections to Scaling at the Fermi-Liquid Fixed Point
• Metallic phase in a two-dimensional disordered Fermi system with singular interactions
• Effective lattice model for collective modes in a Fermi liquid with spin-orbit coupling
• Specific heat of a one-dimensional interacting Fermi system: the role of anomalies
• Coulomb interaction and semimetal-insulator transition in graphene
• Low energy excitations and singular contributions in the thermodynamics of clean Fermi liquids
• Interplay of superconductivity and localization near a 2D ferromagnetic quantum critical point
• Critical quasiparticles in single-impurity and lattice Kondo models
• Interaction effects in 2D electron gas in a random magnetic field: Implications for composite fermions and quantum critical point
• Orbital Dependence of Quasiparticle Lifetimes in Sr2RuO4
• Thermodynamics of Eliashberg theory in the weak-coupling limit
• Zero-bias tunneling anomaly in a clean 2D electron gas caused by smooth density variations
• Self-energy of a nodal fermion in a d-wave superconductor
• Nambu-Eliashberg theory for multi-scale quantum criticality : Application to ferromagnetic quantum criticality in the surface of three dimensional topological insulators
• Universal superdiffusive modes in charged two dimensional liquids
• Spin susceptibility in interacting two-dimensional semiconductors and bilayer systems at first order: Kohn anomalies and spin density wave ordering
• One-dimensional scattering of two-dimensional fermions near quantum criticality
• He3 bi-layers as a simple example of de-confinement
• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• Non-analytic magnetic field dependence of quasi-particle properties of two-dimensional metals
• Fermionization for charge degrees of freedom and bosonization of spin degrees of freedom in the SU(2) slave-boson theory
• Dimensional reduction of the Luttinger-Ward functional for spin-degenerate $D$-dimensional electron gases
• Berry Phase Physics in Free and Interacting Fermionic Systems
• Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals
• Quasiparticle scattering in a superconductor near a nematic critical point: resonance mode and multiple attractive channels
• Nonanalytic Corrections to the Landau Diamagnetic Susceptibility
• Collective mode description for a clean Fermi gas with repulsion in arbitrary dimensions: interaction of spin excitations and its consequences
• Stoner instability revisited: Emergence of local quantum criticality?