39 research outputs found
Renormalization group approach to Fermi Liquid Theory
We show that the renormalization group (RG) approach to interacting fermions
at one-loop order recovers Fermi liquid theory results when the forward
scattering zero sound (ZS) and exchange (ZS) channels are both taken into
account. The Landau parameters are related to the fixed point value of the
``unphysical'' limit of the forward scattering vertex. We specify the
conditions under which the results obtained at one-loop order hold at all order
in a loop expansion. We also emphasize the similarities between our RG approach
and the diagrammatic derivation of Fermi liquid theory.Comment: 4 pages (RevTex) + 1 postcript file, everything in a uuencoded file,
uses epsf (problem with the figure in the first version
High Density Effective Theory Confronts the Fermi Liquid
The high density effective theory recently introduced by Hong and Hsu to
describe ultradense relativistic fermionic matter is used to calculate the
tree-level forward scattering amplitude between two particles at the Fermi
surface. While the direct term correctly reproduces that of the underlying
gauge theory, the exchange term has the wrong sign. The physical consequences
are discussed in the context of Landau's theoretical description of the Fermi
liquid.Comment: 15 pages, 2 figures; conclusion expanded, reference adde
Realistic Electron-Electron Interaction in a Quantum Wire
The form of an effective electron-electron interaction in a quantum wire with
a large static dielectric constant is determined and the resulting properties
of the electron liquid in such a one-dimensional system are described. The
exchange and correlation energies are evaluated and a possibility of a
paramagnetic-ferromagnetic phase transition in the ground state of such a
system is discussed. Low-energy excitations are briefly described.Comment: 10 pages, 6 figure
Is the mean-field approximation so bad? A simple generalization yelding realistic critical indices for 3D Ising-class systems
Modification of the renormalization-group approach, invoking Stratonovich
transformation at each step, is proposed to describe phase transitions in 3D
Ising-class systems. The proposed method is closely related to the mean-field
approximation. The low-order scheme works well for a wide thermal range, is
consistent with a scaling hypothesis and predicts very reasonable values of
critical indices.Comment: 4 page
"quasi-particles" in bosonization theory of interacting fermion liquids at arbitrary dimensions
Within bosonization theory we introduce in this paper a new definition of
"quasi-particles" for interacting fermions at arbitrary space dimenions. In
dimensions higher than one we show that the constructed quasi-particles are
consistent with quasi-particle descriptions in Landau Fermi liquid theory
whereas in one-dimension the quasi-particles" are non-perturbative objects
(spinons and holons) obeying fractional statistics. The more general situation
of Fermi liquids with singular Landau interaction is discussed.Comment: 10 page
The Fermi Liquid as a Renormalization Group Fixed Point: the Role of Interference in the Landau Channel
We apply the finite-temperature renormalization-group (RG) to a model based
on an effective action with a short-range repulsive interaction and a rotation
invariant Fermi surface. The basic quantities of Fermi liquid theory, the
Landau function and the scattering vertex, are calculated as fixed points of
the RG flow in terms of the effective action's interaction function. The
classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter
equation and amount to summing direct particle-hole ladder diagrams, neglect
the zero-angle singularity in the exchange particle-hole loop. As a
consequence, the antisymmetry of the forward scattering vertex is not
guaranteed and the amplitude sum rule must be imposed by hand on the components
of the Landau function. We show that the strong interference of the direct and
exchange processes of particle-hole scattering near zero angle invalidates the
ladder approximation in this region, resulting in temperature-dependent
narrow-angle anomalies in the Landau function and scattering vertex. In this RG
approach the Pauli principle is automatically satisfied. The consequences of
the RG corrections on Fermi liquid theory are discussed. In particular, we show
that the amplitude sum rule is not valid.Comment: 25 pages, RevTeX 3.
Renormalization group study of interacting electrons
The renormalization-group (RG) approach proposed earlier by Shankar for
interacting spinless fermions at is extended to the case of non-zero
temperature and spin. We study a model with -invariant short-range
effective interaction and rotationally invariant Fermi surface in two and three
dimensions. We show that the Landau interaction function of the Fermi liquid,
constructed from the bare parameters of the low-energy effective action, is RG
invariant. On the other hand, the physical forward scattering vertex is found
as a stable fixed point of the RG flow. We demonstrate that in and 3, the
RG approach to this model is equivalent to Landau's mean-field treatment of the
Fermi liquid. We discuss subtleties associated with the symmetry properties of
the scattering amplitude, the Landau function and the low-energy effective
action. Applying the RG to response functions, we find the compressibility and
the spin susceptibility as fixed points.Comment: 11 pages, RevTeX 3.0, 2 PostScript figure
Atomic Dark Matter
We propose that dark matter is dominantly comprised of atomic bound states.
We build a simple model and map the parameter space that results in the early
universe formation of hydrogen-like dark atoms. We find that atomic dark matter
has interesting implications for cosmology as well as direct detection:
Protohalo formation can be suppressed below for weak scale dark matter due to Ion-Radiation interactions in the
dark sector. Moreover, weak-scale dark atoms can accommodate hyperfine
splittings of order 100 \kev, consistent with the inelastic dark matter
interpretation of the DAMA data while naturally evading direct detection
bounds.Comment: 17 pages, 3 figure
Scaling Of Chiral Lagrangians And Landau Fermi Liquid Theory For Dense Hadronic Matter
We discuss the Fermi-liquid properties of hadronic matter derived from a
chiral Lagrangian field theory in which Brown-Rho (BR) scaling is incorporated.
We identify the BR scaling as a contribution to Landau's Fermi liquid
fixed-point quasiparticle parameter from "heavy" isoscalar meson degrees of
freedom that are integrated out from a low-energy effective Lagrangian. We show
that for the vector (convection) current, the result obtained in the chiral
Lagrangian approach agrees precisely with that obtained in the
semi-phenomenological Landau-Migdal approach. This precise agreement allows one
to determine the Landau parameter that enters in the effective nucleon mass in
terms of the constant that characterizes BR scaling. When applied to the weak
axial current, however, these two approaches differ in a subtle way. While the
difference is small numerically, the chiral Lagrangian approach implements
current algebra and low-energy theorems associated with the axial response that
the Landau method misses and hence is expected to be more predictive.Comment: 39 pages, latex with 4 eps figure, modified addresses and reference
A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
We provide a framework for analyzing the problem of interacting electrons in
a ballistic quantum dot with chaotic boundary conditions within an energy
(the Thouless energy) of the Fermi energy. Within this window we show that the
interactions can be characterized by Landau Fermi liquid parameters. When ,
the dimensionless conductance of the dot, is large, we find that the disordered
interacting problem can be solved in a saddle-point approximation which becomes
exact as (as in a large-N theory). The infinite theory shows a
transition to a strong-coupling phase characterized by the same order parameter
as in the Pomeranchuk transition in clean systems (a spontaneous
interaction-induced Fermi surface distortion), but smeared and pinned by
disorder. At finite , the two phases and critical point evolve into three
regimes in the plane -- weak- and strong-coupling regimes separated
by crossover lines from a quantum-critical regime controlled by the quantum
critical point. In the strong-coupling and quantum-critical regions, the
quasiparticle acquires a width of the same order as the level spacing
within a few 's of the Fermi energy due to coupling to collective
excitations. In the strong coupling regime if is odd, the dot will (if
isolated) cross over from the orthogonal to unitary ensemble for an
exponentially small external flux, or will (if strongly coupled to leads) break
time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we
are treating charge-channel instabilities in spinful systems, leaving
spin-channel instabilities for future work. No substantive results are
change