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Register a new userMany-body Theory vs Simulations for the pseudogap in the Hubbard model
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Added by
Andre-Marie Tremblay
Publication date
1999
fields
Physics
and research's language is
English
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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.
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Understanding quantum many-body states of correlated electrons is one main theme in modern condensed matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, has been recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping, to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Phys. Rev. X 8, 031082 (2018)], complemented with independent determinant quantum Monte Carlo (DQMC) offer a powerful combination of tools for this purpose. XTRG provides full and accurate access to the density matrix and thus various spin and charge correlations, down to unprecedented low temperature of few percents of the fermion tunneling energy scale. We observe excellent agreement with ultracold fermion measurements at both half-filling and finite-doping, including the sign-reversal behavior in spin correlations due to formation of magnetic polarons, and the attractive hole-doublon and repulsive hole-hole pairs that are responsible for the peculiar bunching and antibunching behavior of the antimoments.
In this thesis, I present a non-perturbative approach to the single-band attractive Hubard model which is an extension of previous work by Vilk and Tremblay on the repulsive model. Exact results are derived in the general context of functional derivative approaches to many-body theories. The first step of the approximation is based on a local field type ansatz. All physical quantities can be expressed as a function of double-occupancy (in addition to temperature and filling). Double-occupancy is determined without adjustable parameter by imposing the Pauli principle and a crucial sum-rule, making the first step of the approximation Two-Particle Self-Consistent. The final expression for the self-energy is obtained by calculating the low-frequency part of the exact expression with the two-particle correlation, Green function and renormalized vertex obtained in the first step of the approximation. The Mermin-Wagner theorem in two dimensions is automatically satisfied. Application of this non-perturbative many-body approach to the intermediate coupling regime shows quantitative agreement with quantum Monte Carlo calculations. Both approaches predict the existence of a pseudogap in the single-particle spectral weight. I present some physical properties, such as correlation lengths, superfluid density, and characteristic pair fluctuation energy, to highlight the origin of the pseudogap in the weak to intermediate coupling regime. These results suggest that two-dimensional systems that are described by a symmetry group larger than SO(2) could have a larger region of pseudogap behavior. High-temperature superconductors may belong to that category of systems.
We analyze the pseudogap phenomenon of hole-doped cuprates via a Feynman-diagrammatic inspection of the Hubbard model. Our approach captures the pivotal interplay between Mott localization and Fermi surface topology beyond weak-coupling spin fluctuations, which open a spectral gap near hot spots. We show that strong coupling and particle-hole asymmetry give rise to another mechanism: the spin-fermion vertex develops a large imaginary part. While its real part always suppresses the electronic lifetime, the imaginary part has a twofold effect. For antinodal fermions a gap opening is boosted; conversely, around the node Fermi arcs are protected.
The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model, based on exact results or controlled approximate solutions in various limits, for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions, although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions.
We calculate the spectral weight of the one- and two-dimensional Hubbard models, by performing exact diagonalizations of finite clusters and treating inter-cluster hopping with perturbation theory. Even with relatively modest clusters (e.g. 12 sites), the spectra thus obtained give an accurate description of the exact results. Thus, spin-charge separation (i.e. an extended spectral weight bounded by singularities) is clearly recognized in the one-dimensional Hubbard model, and so is extended spectral weight in the two-dimensional Hubbard model.
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