107 research outputs found
Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
A new approach to the single-band Hubbard model is described in the general
context of many-body theories. It is based on enforcing conservation laws, the
Pauli principle and a number of crucial sum-rules. More specifically, spin and
charge susceptibilities are expressed, in a conserving approximation, as a
function of two constant irreducible vertices whose values are found
self-consistently. The Mermin-Wagner theorem in two dimensions is automatically
satisfied. The effect of collective modes on single-particle properties is then
obtained by a paramagnon-like formula that is consistent with the two-particle
properties in the sense that the potential energy obtained from is
identical to that obtained using the fluctuation-dissipation theorem for
susceptibilities. The vertex corrections are included through constant
irreducible vertices. The theory is in quantitative agreement with Monte Carlo
simulations for both single-particle and two-particle properties. In the
two-dimensional renormalized classical regime, spin fluctuations lead to
precursors of antiferromagnetic bands (shadow bands) and to the destruction of
the Fermi-liquid quasiparticles in a wide temperature range above the
zero-temperature phase transition. The analogous phenomenon of pairing
pseudogap can occur in the attractive model in two dimensions when the pairing
fluctuations become critical. Other many-body approaches are critically
compared. It is argued that treating the spin fluctuations as if there was a
Migdal's theorem can lead to wrong predictions, in particular with regard to
the the single-particle pseudogap.Comment: Small changes to conform to published version. Main text 33 pages.
Appendices 16 pages. 11 PS figures epsf/Latex. Section on the single-particle
pseudogap can be read independentl
Slave spin cluster mean field theory away from half-filling: Application to the Hubbard and the extended Hubbard Model
A new slave-spin representation of fermion operators has recently been
proposed for the half-filled Hubbard model. We show that with the addition of a
gauge variable, the formalism can be extended to finite doping. The resulting
spin problem can be solved using the cluster mean-field approximation. This
approximation takes short-range correlations into account by exact
diagonalization on the cluster, whereas long-range correlations beyond the size
of clusters are treated at the mean-field level. In the limit where the cluster
has only one site and the interaction strength is infinite, this approach
reduces to the Gutzwiller approximation. There are some qualitative differences
when the size of the cluster is finite. We first compute the critical for
the Mott transition as a function of a frustrating second-neighbor interaction
on lattices relevant for various correlated systems, namely the cobaltites, the
layered organic superconductors and the high-temperature superconductors. For
the triangular lattice, we also study the extended Hubbard model with
nearest-neighbor repulsion. In additionto a uniform metallic state, we find a
charge density wave in a broad doping regime,
including commensurate ones. We find that in the large limit, intersite
Coulomb repulsion strongly suppresses the single-particle weight of the
metallic state.Comment: 10 pages, 11 figures, submitted to PR
Many-body Theory vs Simulations for the pseudogap in the Hubbard model
The opening of a critical-fluctuation induced pseudogap (or precursor
pseudogap) in the one-particle spectral weight of the half-filled
two-dimensional Hubbard model is discussed. This pseudogap, appearing in our
Monte Carlo simulations, may be obtained from many-body techniques that use
Green functions and vertex corrections that are at the same level of
approximation. Self-consistent theories of the Eliashberg type (such as the
Fluctuation Exchange Approximation) use renormalized Green functions and bare
vertices in a context where there is no Migdal theorem. They do not find the
pseudogap, in quantitative and qualitative disagreement with simulations,
suggesting these methods are inadequate for this problem. Differences between
precursor pseudogaps and strong-coupling pseudogaps are also discussed.Comment: Accepted, Phys. Rev. B15 15Mar00. Expanded version of original
submission, Latex, 8 pages, epsfig, 5 eps figures (Last one new). Discussion
on fluctuation and strong coupling induced pseudogaps expande
Non-perturbative approach to the attractive Hubbard model
A non-perturbative approach to the single-band attractive Hubbard model is
presented in the general context of functional derivative approaches to
many-body theories. As in previous work on the repulsive model, the first step
is based on a local-field type ansatz, on enforcement of the Pauli principle
and a number of crucial sum-rules. The Mermin-Wagner theorem in two dimensions
is automatically satisfied. At this level, two-particle self-consistency has
been achieved. In the second step of the approximation, an improved expression
for the self-energy is obtained by using the results of the first step in an
exact expression for the self-energy where the high- and low-frequency
behaviors appear separately. The result is a cooperon-like formula. The
required vertex corrections are included in this self-energy expression, as
required by the absence of a Migdal theorem for this problem. Other approaches
to the attractive Hubbard model are critically compared. Physical consequences
of the present approach and agreement with Monte Carlo simulations are
demonstrated in the accompanying paper (following this one).Comment: Revtex, 19 page
Evolution of the pairing pseudogap in the spectral function with interplane anisotropy
We study the pairing pseudogap in the spectral function as a function of
interplane coupling. The analytical expressions for the self-energy in the
critical regime are obtained for any degree of anisotropy. The frequency
dependence of the self-energy is found to be qualitatively different in two and
three dimensions, and the crossover from two to three dimensional behavior is
discussed. In particular, by considering the anisotropy of the Fermi velocity
and gap along the Fermi surface, we can qualitatively explain recent
photoemission experiments on high temperature superconductors concerning the
temperature dependent Fermi arcs seen in the pseudogap phase.Comment: 20 pages, revtex, 5 encapsulated postscript figures include
Role of symmetry and dimension on pseudogap phenomena
The attractive Hubbard model in d=2 is studied through Monte Carlo
simulations at intermediate coupling. There is a crossover temperature
where a pseudogap appears with concomitant precursors of Bogoliubov
quasiparticles that are not local pairs. The pseudogap in occurs
in the renormalized classical regime when the correlation length is larger than
the direction-dependent thermal de Broglie wave length, The ratio for the pseudogap may be made
arbitrarily large when the system is close to a point where the order parameter
has SO(n) symmetry with n>2. This is relevant in the context of SO(5) theories
of high but has more general applicability.Comment: 4 pages, LaTeX, 4 epsf figures included. Corrected to agree with
published version. Main change, one new figur
Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects
The temperature-dependent uniform magnetic susceptibility of interacting
electrons in one dimension is calculated using several methods. At low
temperature, the renormalization group reaveals that the Luttinger liquid spin
susceptibility approaches zero temperature with an infinite slope
in striking contrast with the Fermi liquid result and with the behavior of the
compressibility in the absence of umklapp scattering. This effect comes from
the leading marginally irrelevant operator, in analogy with the Heisenberg spin
1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher
temperature reveal that non-logarithmic terms are important in that regime.
These contributions are evaluated from an effective interaction that includes
the same set of diagrams as those that give the leading logarithmic terms in
the renormalization group approach. Comments on the third law of thermodynamics
as well as reasons for the failure of approaches that work in higher dimensions
are given.Comment: 21 pages, latex including 5 eps figure
Self-Consistent Random Phase Approximation - Application to the Hubbard Model for finite number of sites
Within the 1D Hubbard model linear closed chains with various numbers of
sites are considered in Self Consistent Random Phase Approximation (SCRPA).
Excellent results with a minimal numerical effort are obtained for 2+4n sites
cases, confirming earlier results with this theory for other models. However,
the 4n sites cases need further considerations. SCRPA solves the two sites
problem exactly. It therefore contains the two electrons and high density Fermi
gas limits correctly.Comment: 17 pages, 17 figure
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