Based on the Keldysh formalism, we derive an effective Boltzmann equation for a quasiparticle constrained within a particular Fermi surface in an interacting Fermi liquid. This provides a many-body derivation of Berry curvatures in electron dynamics with spin-orbit coupling, which has received much attention in recent years in noninteracting models. As is well known, the Berry curvature in momentum space modifies naïve band dynamics via an "artificial magnetic field" in momentum space. Our Fermi liquid formulation completes the reinvention of modified band dynamics by introducing in addition an artificial electric field, related to Berry curvature in frequency and momentum space. We show explicitly how the artificial electric field affects the renormalization factor and transverse conductivity of interacting U(1) Fermi liquids with nondegenerate bands.
Based on the Keldysh formalism, we derive an effective Boltzmann equation for a quasiparticle constrained within a particular Fermi surface in an interacting Fermi liquid. This provides a many-body derivation of Berry curvatures in electron dynamics with spin-orbit coupling, which has received much attention in recent years in noninteracting models. As is well known, the Berry curvature in momentum space modifies naïve band dynamics via an "artificial magnetic field" in momentum space. Our Fermi liquid formulation completes the reinvention of modified band dynamics by introducing in addition an artificial electric field, related to Berry curvature in frequency and momentum space. We show explicitly how the artificial electric field affects the renormalization factor and transverse conductivity of interacting U(1) Fermi liquids with nondegenerate bands.
We consider the response of the density of a fermion ensemble to an applied weak static magnetic field. It is known that, for a noninteracting Fermi gas, this response is fully characterized by the Fermi volume and the Berry curvature on the Fermi surface. Here we show the same result holds for interacting fermions, including a Fermi liquid and a non-Fermi liquid, to all orders in perturbation theory. Our result relies only on the assumption of a well-defined Fermi surface and the general analytic properties of quantum field theory, and is completely model independent.
We develop a mean-field theory of the 1D spin-1 antiferromagnetic Heisenberg model, using a two-orbital fermionic representation for the spin-1 operators. Two ansatz with different orbital pairing symmetries are discussed and the projected mean-field ground states with their corresponding parent Hamiltonians have also been obtained. Then we study the U(1) spin liquid state with large spinon Fermi surfaces. The physical conductivity obtained through Ioffe-Larkin composition rule can support surface plasmon modes propagating along the interface between the spin liquid and a linear medium, which can be excited using a Kretschmann-Raether configuration. Next we generalize the linear current response to including nonlinear effects under the perturbation of a time dependent but spatially uniform electric field in the framework of an effective U(1) gauge theory derived through a Fermi-liquid-like approach. The nonlinear susceptibility can support waves with triple frequency inside the spin liquids through the process of third harmonic generation. As a byproduct during the Fermi-liquid approach, we generalize the standard Landau Fermi liquid theory to describe the intrinsic anomalous Hall conductivity, based on some general symmetric considerations. Fitting result of the anomalous Hall conductivity is well consistent with the experimental data, and behaves better in lower frequency range than the simple two-band model.
The Fermi-liquid transport theory of electrical conductivity formulated by Eliashberg [Zh. Eksp. Teor. Fiz. 41, 1241 (1961)] is further developed, using the analytic continuation of the finite-temperature Ward-Takahashi relations obtained by the present author [Ann. Phys. (N.Y.) 173, 226 (1987)] to maintain the theoretical consistency of approximation schemes for solving the Bethe-Salpeter equation. In particular, the finite-temperature Ward-Takahashi relations corresponding to the local conservation of the electron number density and to the conservation of the electron momentum are considered. A general expression for the electrical conductivity in terms of the proper vertex part is also obtained. In the formula, cancellation of the quasiparticle renormalization factors at the Fermi surface is explicitly shown in a general way without assuming a particular model. In the case that the electrons are scattered by phonons, the formula gives the Gr\"uneisen-Bloch formula for the on-shell phonons. For the impurity resistivity, the theory of Edwards [Philos. Mag. 3, 1020 (1958)] is developed to finite temperature by introducing a hypothetical boson field that replaces the impurity averaging.
The Fermi-liquid approach generalized to superfluid systems is used to derive general formulas for the normal and abnormal distribution functions (DF) for quasiparticles of a superfluid Fermi liquid (SFL) consisting of electrically neutral fermions with spin-triplet pairing (the spin of a pair s=1, the orbital angular momentum l of the pair being an arbitrary odd number) in a static uniform magnetic field, taking into account the Landau spin-exchange Fermi-liquid interaction at temperatures 0<T<Tc (Tc is the temperature of phase transition from the normal to the superfluid state). In deriving the DF, the explicit form of the energy functional (EF) for SFL is not used. A system of coupled equations is obtained for the order parameter, energy of quasiparticles, and effective magnetic field for the SFL under investigation in the case of an EF quadratic in DF. The obtained DF and the system of equations are applicable for describing both unitary and nonunitary phases of superfluid He3 in a magnetic field, e.g., for determining the magnetization and magnetic susceptibility of these phases.
We develop, in this dissertation, a theoretical formalism for Fermi liquids by exploiting an underlying algebro-geometric structure described by the group of canonical transformations of a single particle phase space. This infinite-dimensional group governs the space of states of zero temperature Fermi liquids and thereby allows us to write down a nonlinear, bosonized action that reproduces Landau's kinetic theory in the classical limit. Upon quantizing, we obtain a systematic effective field theory as an expansion in nonlinear and higher derivative corrections suppressed by the Fermi momentum pF , without the need to introduce artificial momentum scales through, e.g., decomposition of the Fermi surface into patches. We find that Fermi liquid theory can essentially be thought of as a non-trivial representation of the Lie group of canonical transformations, bringing it within the fold of effective theories in many-body physics whose structure is determined by symmetries. We survey the benefits and limitations of this geometric formalism in the context of scaling, diagrammatic calcu- lations, scattering and interactions, coupling to background gauge fields, etc. After setting up a path to extending this formalism to include superconducting and magnetic phases, as well as applications to the problem of non-Fermi liquids, we conclude with a discussion on possible future directions for Fermi surface physics, and more broadly, the usefulness of diffeomorphism groups in condensed matter physics.
In the present work, we implement an explicit two-loop renormalization of a two-dimensional flat Fermi surface (FS) in the framework of a field theoretical renormalization group approach (RG). In our scheme, we derive the RG equations for both the coupling functions and Fermi energy. In this way, we are able to probe the existence of spin-charge separation by showing that the low-energy sector of the system is in fact a non-Fermi liquid. In addition, associating the true interacting FS to the infrared stable (IR) fixed point of the Fermi energy, we demonstrate here that it either acquires a small curvature and behaves as a "Luttinger liquid" or it suffers a truncation in k-space depicting an insulating spin liquid.