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Register a new userEfficient slave-boson approach for multiorbital two-particle response functions and superconductivity
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We develop an efficient approach for computing two-particle response functions and interaction vertices for multiorbital strongly correlated systems based on fluctuation around rotationally-invariant slave-boson saddle-point. The method is applied to the degenerate three-orbital Hubbard-Kanamori model for investigating the origin of the s-wave orbital antisymmetric spin-triplet superconductivity in the Hunds metal regime, previously found in the dynamical mean-field theory studies. By computing the pairing interaction considering the particle-particle and the particle-hole scattering channels, we identify the mechanism leading to the pairing instability around Hunds metal crossover arises from the particle-particle channel, containing the local electron pair fluctuation between different particle-number sectors of the atomic Hilbert space. On the other hand, the particle-hole spin fluctuations induce the s-wave pairing instability before entering the Hunds regime. Our approach paves the way for investigating the pairing mechanism in realistic correlated materials.
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We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our Ansatz is an optimized linear superposition of Affleck-Kennedy-Lieb-Tasaki valence bond states, rendering the combination a valence bond liquid dubbed Orbital Resonant Valence Bond. We show that the undoped (one electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Andersons resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths -- W the carriers bandwidth -- could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.
The conserving approximation scheme to many-body problems was developed by Kadanoff and Baym using the functional-derivative approach. Another approach for the Hubbard model also satisfies conservation laws, but in addition it satisfies the Pauli principle and a number of sum rules. A concise formal derivation of that approach, using functional derivatives, is given in this conference paper to highlight formal analogies and differences with conserving approximations.
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.
Atomic repulsion $U_d$ on the Cu site in high T$_c$ cuprates is large but, surprisingly, some important properties are consistent with moderate couplings. The time dependent perturbation theory with slave particles is therefore formulated in the $U_dtoinfty$ limit for the metallic phase in the physically relevant regime of the three-band Emery model. The basic theory possesses the local gauge invariance asymptotically but its convergence is fast when the average occupation of the Cu-site is small. The leading orders exhibit the band narrowing and the dynamic Cu/O$_2$ charge transfer disorder. The effective local repulsion between particles on oxygen sites is shown to be moderate in the physical regime under consideration. It enhances the coherent incommensurate SDW correlations. The latter compete with the Cu/O$_2$ charge transfer disorder, in agreement with basic observations in high T$_c$ cuprates.
A rational representation for the self-energy is explored to interpolate the solution of the Anderson impurity model in general orbitally degenerate case. Several constrains such as the Friedels sum rule, high--frequency moments and the value of quasiparticle residue are used to establish the equations for the coefficients of the interpolation. We test two fast techniques, the slave--boson mean--field and the Hubbard I approximation to determine the coefficients. The obtained self--energies are compared with the results of numerically exact Quantum Monte Carlo method. We find that using the slave--boson mean--field approach we can construct an accurate self--energy for all frequencies via the proposed interpolation procedure.
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