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Letz, M.; Marsiglio, F.

doi:10.1023/a:1021822224492

Cited by 4 publications

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“…In one and two dimensions, for low temperatures, the system is always unstable towards a condensation into an infinite lifetime two-particle bound state. For two dimensions this was demonstrated for a non self-consistent, non conserving theory by Schmitt-Rink, et al [8], and we [9] have recently shown similar physics is encountered when a fully conserving theory is used. However, the self-consistent theories, at least to the minimum temperatures that we have been able to access, do not show similar physics.…”

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confidence: 71%

Spectral properties of the attractive Hubbard model

Letz

Gooding

1998

Journal of Physics and Chemistry of Solids

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Deviations from Fermi liquid behavior are well documented in the normal state of the cuprate superconductors, and some of these differences are possibly related to pre-formed pairs appearing at temperatures above Tc. In order to test these ideas we have investigated the attractive Hubbard model within a self-consistent, conserving ladder approximation. In this version of the theory, no feature is present which can be related to the pseudo gap found in the high-Tc materials. Further, the interactions between two-particle bound states change the physics of the superconducting instability in a profound fashion, and lead to a completely different phenomenology that one predicts based on the non-self-consistent version of the same theory.

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confidence: 71%

Spectral properties of the attractive Hubbard model

Letz

Gooding

1998

Journal of Physics and Chemistry of Solids

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“…( 1) and ( 3). This is the main numerical difficulty for any self-consistent approximation; only in the last years self-consistent approaches have been applied to the study of high T c superconductors [27,28,29,30] and nuclear matter [4,5,7,8,9]. Some calculations are performed in the imaginary time formalism [27,28] which requires a numerical procedure for the analytical continuation to calculate the spectral function.…”

Section: Appendix A: Numerical Methodsmentioning

confidence: 99%

“…To deal with the off-shell propagation a numerical parameterization of the energy dependence of the spectral function A(p, ω) by a set of Gaussians has been used [4,8]. Alternatively, the spectral function can be represented as a sum of δ functions [9,30]. The above two methods can be easily applied at zero temperature, where a narrow Gausian or one of the δ functions describes the quasi-particle peak for momenta close to the Fermi surface.…”

Section: Appendix A: Numerical Methodsmentioning

confidence: 99%

One-body properties of nuclear matter with off-shell propagation

Božek

2002

Phys. Rev. C

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“…This result may be understood, at least in part, in terms the non self-consistent, non conserving theory of Ref. [7] -the fermion density is suppressed as one approaches the Thouless criterion, and all quasiparticles form two-particle bound states (this behaviour survives when one treats the non self-consistent theory in a conserving approximation [8]). Our simplified self-consistent, conserving theory shows that this physics is completely lost when interactions between the pairs are included -now one finds, similar to a usual fermi liquid, that the lifetimes of quasiparticles are longest at the fermi energy.…”

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Quasiparticle lifetime behaviour in a simplified self-consistent T-matrix treatment of the attractive Hubbard model in 2D

Letz

Gooding

1997

Physica B: Condensed Matter

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The attractive Hubbard model on a 2-D square lattice is studied at low electronic densities using the ladder approximation for the pair susceptibility. This model includes (i) the short coherence lengths known to exist experimentally in the cuprate superconductors, and (ii) two-particle bound states that correspond to electron pairs. We study the quasiparticle lifetimes in both non self-consistent and self-consistent theories, the latter including interactions between the pairs. We find that if we include the interactions between pairs the quasiparticle lifetimes vary approximately linearly with the inverse temperature, consistent with experiment. Keywords: attractive Hubbard model; quasiparticle propertiesNumerous recent experiments (e.g., neutrons, ARPES, optical, NMR) have shown that in the high T c cuprate superconductors a so-called pseudogap is present [1]. This has led to proposals that electron pairs form at temperatures well above the superconducting transition temperature. However, possibly due to phase fluctuations, a macroscopic phase coherent wave function is not formed, so superconductivity is not encountered [2].This physics motivates our study of the attractive Hubbard model. The Hamiltonian for this system iswhere the lattice sites of a 2-D square lattice are labeled by {i}, the lattice fermion operators are denoted by c i,σ , and neighbouring sites are represented by ij . For any nonzero | U |, two-particle bound states appear, and are physically related to a pair of electrons lowering the system's energy when they exist on the same lattice site. This is certainly the simplest example of a model Hamiltonian which allows for one to study the interactions between such electron pairs. Further, using a Gorkov derivation of the Ginzburg-Landau equations for an s-wave superconductor, one can show that for the values of | U | /W that we are considering, W = 8t being the (noninteracting) bandwidth, this model also reproduces the short coherence lengths of the Cooper pairs found in the high T c cuprate superconductors [3].We employ the Brueckner Hartree-Fock theory to solve the Bethe-Salpeter equation for the 2D attractive Hubbard model in the ladder approximation [4], reliable for this model at low electron (or hole) densities. This affords us the opportunity to investigate the influence of preformed pairs with arbitrary lifetimes on the normal state properties. Haussmann has argued [5] that when one solves this model in this approximation self consistently, one will include pair-pair interactions. These interactions will be, in first order, of a repulsive nature between different pairs.

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Cited by 4 publications

References 13 publications

Spectral properties of the attractive Hubbard model

Spectral properties of the attractive Hubbard model

One-body properties of nuclear matter with off-shell propagation

Quasiparticle lifetime behaviour in a simplified self-consistent T-matrix treatment of the attractive Hubbard model in 2D

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