2,425 research outputs found
Fermi Surface of the 2D Hubbard Model at Weak Coupling
We calculate the interaction-induced deformation of the Fermi surface in the
two-dimensional Hubbard model within second order perturbation theory. Close to
half-filling, interactions enhance anisotropies of the Fermi surface, but they
never modify the topology of the Fermi surface in the weak coupling regime.Comment: 4 pages, LaTeX2e, 5 embedded EPS figures, accepted to be published in
Z. Phys.
Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model
We analyze the competition between antiferromagnetism and superconductivity
in the two-dimensional Hubbard model by combining a functional renormalization
group flow with a mean-field theory for spontaneous symmetry breaking.
Effective interactions are computed by integrating out states above a scale
Lambda_{MF} in one-loop approximation, which captures in particular the
generation of an attraction in the d-wave Cooper channel from fluctuations in
the particle-hole channel. These effective interactions are then used as an
input for a mean-field treatment of the remaining low-energy states, with
antiferromagnetism, singlet superconductivity and triplet pi-pairing as the
possible order parameters. Antiferromagnetism and superconductivity suppress
each other, leaving only a small region in parameter space where both orders
can coexist with a sizable order parameter for each. Triplet pi-pairing appears
generically in the coexistence region, but its feedback on the other order
parameters is very small.Comment: 28 pages, 14 figure
Critical temperature and Ginzburg region near a quantum critical point in two-dimensional metals
We compute the transition temperature and the Ginzburg temperature
above near a quantum critical point at the boundary of an
ordered phase with a broken discrete symmetry in a two-dimensional metallic
electron system. Our calculation is based on a renormalization group analysis
of the Hertz action with a scalar order parameter. We provide analytic
expressions for and as a function of the non-thermal control
parameter for the quantum phase transition, including logarithmic corrections.
The Ginzburg regime between and occupies a sizable part of
the phase diagram.Comment: 5 pages, 1 figur
Incommensurate nematic fluctuations in the two-dimensional Hubbard model
We analyze effective d-wave interactions in the two-dimensional extended
Hubbard model at weak coupling and small to moderate doping. The interactions
are computed from a renormalization group flow. Attractive d-wave interactions
are generated via antiferromagnetic spin fluctuations in the pairing and charge
channels. Above Van Hove filling, the d-wave charge interaction is maximal at
incommensurate diagonal wave vectors, corresponding to nematic fluctuations
with a diagonal modulation. Below Van Hove filling a modulation along the
crystal axes can be favored. The nematic fluctuations are enhanced by the
nearest-neighbor interaction in the extended Hubbard model, but they always
remain smaller than the dominant antiferromagnetic, pairing, or charge density
wave fluctuations.Comment: 8 pages, 4 figures; figures improve
Mean-field theory for symmetry-breaking Fermi surface deformations on a square lattice
We analyze a mean-field model of electrons with pure forward scattering
interactions on a square lattice which exhibits spontaneous Fermi surface
symmetry breaking with a d-wave order parameter: the surface expands along the
kx-axis and shrinks along the ky-axis (or vice versa). The symmetry-broken
phase is stabilized below a dome-shaped transition line Tc(mu), with a maximal
Tc near van Hove filling. The phase transition is usually first order at the
edges of the transition line, and always second order around its center. The
d-wave compressibility of the Fermi surface is however strongly enhanced even
near the first order transition down to zero temperature. In the weak coupling
limit the phase diagram is fully determined by a single non-universal energy
scale, and hence dimensionless ratios of different characteristic quantities
are universal. Adding a uniform repulsion to the forward scattering
interaction, the two tricritical points at the ends of the second order
transition line are shifted to lower temperatures. For a particularly favorable
choice of hopping and interaction parameters one of the first order edges is
replaced completely by a second order transition line, leading to a quantum
critical point.Comment: 23 pages, 8 figure
Singular order parameter interaction at nematic quantum critical point in two dimensional electron systems
We analyze the infrared behavior of effective N-point interactions between
order parameter fluctuations for nematic and other quantum critical electron
systems with a scalar order parameter in two dimensions. The interactions
exhibit a singular momentum and energy dependence and thus cannot be
represented by local vertices. They diverge for all N greater or equal 4 in a
collinear static limit, where energy variables scale to zero faster than
momenta, and momenta become increasingly collinear. The degree of divergence is
not reduced by any cancellations and renders all N-point interactions marginal.
A truncation of the order parameter action at quartic or any other finite order
is therefore not justified. The same conclusion can be drawn for the effective
action describing fermions coupled to a U(1) gauge field in two dimensions.Comment: 18 pages, 1 figur
Competition of Fermi surface symmetry breaking and superconductivity
We analyze a mean-field model of electrons on a square lattice with two types
of interaction: forward scattering favoring a d-wave Pomeranchuk instability
and a BCS pairing interaction driving d-wave superconductivity. Tuning the
interaction parameters a rich variety of phase diagrams is obtained. If the BCS
interaction is not too strong, Fermi surface symmetry breaking is stabilized
around van Hove filling, and coexists with superconductivity at low
temperatures. For pure forward scattering Fermi surface symmetry breaking
occurs typically via a first order transition at low temperatures. The presence
of superconductivity reduces the first order character of this transition and,
if strong enough, can turn it into a continuous one. This gives rise to a
quantum critical point within the superconducting phase. The superconducting
gap tends to suppress Fermi surface symmetry breaking. For a relatively strong
BCS interaction, Fermi surface symmetry breaking can be limited to intermediate
temperatures, or can be suppressed completely by pairing.Comment: 14 pages, 10 figure
Electrical resistivity near Pomeranchuk instability in two dimensions
We analyze the DC charge transport in the quantum critical regime near a
d-wave Pomeranchuk instability in two dimensions. The transport decay rate is
linear in temperature everywhere on the Fermi surface except at cold spots on
the Brillouin zone diagonal. For pure systems, this leads to a DC resistivity
proportional to T^{3/2} in the low-temperature limit. In the presence of
impurities the residual impurity resistance at T=0 is approached linearly at
low temperatures.Comment: 9 pages, no figure
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