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Benchmark of a modified Iterated Perturbation Theory approach on the 3d FCC lattice at strong coupling
The Dynamical Mean-Field theory (DMFT) approach to the Hubbard model requires
a method to solve the problem of a quantum impurity in a bath of
non-interacting electrons. Iterated Perturbation Theory (IPT) has proven its
effectiveness as a solver in many cases of interest. Based on general
principles and on comparisons with an essentially exact Continuous-Time Quantum
Monte Carlo (CTQMC) solver, here we show that the standard implementation of
IPT fails away from half-filling when the interaction strength is much larger
than the bandwidth. We propose a slight modification to the IPT algorithm that
replaces one of the equations by the requirement that double occupancy
calculated with IPT gives the correct value. We call this method IPT-. We
recover the Fermi liquid ground state away from half-filling. The Fermi liquid
parameters, density of states, chemical potential, energy and specific heat on
the FCC lattice are calculated with both IPT- and CTQMC as benchmark
examples. We also calculated the resistivity and the optical conductivity
within IPT-. Particle-hole asymmetry persists even at coupling twice the
bandwidth. Several algorithms that speed up the calculations are described in
appendices.Comment: 17 pages, 15 figures, minor changes to improve clarit
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
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