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Register a new userFLEX+DMFT approach to the $d$-wave superconducting phase diagram of the two-dimensional Hubbard model
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The dynamical mean-field theory (DMFT) combined with the fluctuation exchange (FLEX) method, namely FLEX+DMFT, is an approach for correlated electron systems to incorporate both local and non-local long-range correlations in a self-consistent manner. We formulate FLEX+DMFT in a systematic way starting from a Luttinger-Ward functional, and apply it to study the $d$-wave superconductivity in the two-dimensional repulsive Hubbard model. The critical temperature ($T_c$) curve obtained in the FLEX+DMFT exhibits a dome structure as a function of the filling, which has not been clearly observed in the FLEX approach alone. We trace back the origin of the dome to the local vertex correction from DMFT that renders a filling dependence in the FLEX self-energy. We compare the results with those of GW+DMFT, where the $T_c$-dome structure is qualitatively reproduced due to the same vertex correction effect, but a crucial difference from FLEX+DMFT is that $T_c$ is always estimated below the N{e}el temperature in GW+DMFT. The single-particle spectral function obtained with FLEX+DMFT exhibits a double-peak structure as a precursor of the Hubbard bands at temperature above $T_c$.
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We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the $d_{x^2-y^2}$ superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half-filling. We find a change in sign of the vertex contributions to $d_{xy}$ superconductivity from repulsive near half filling to attractive at large doping. $p$-wave superconductivity is not found at the parameters we study, and $s$-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase $T_c$.
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur at half-filling when 4V > U gives way to a d_{xy} -wave superconducting instability away from half-filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive and a range of on-site repulsive interaction. In addition, when nesting is further suppressed and in presence of a nearest-neighbor attraction, a triplet time-reversal breaking (p_x + ip_y)-wave pairing instability emerges, competing with the d_{x2+y2} pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (p_x +ip_y)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while d_{xy}-pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.
Here we have developed a FLEX+DMFT formalism, where the symmetry properties of the system are incorporated by constructing a SO(4) generalization of the conventional fluctuation-exchange approximation (FLEX) coupled self-consistently to the dynamical mean-field theory (DMFT). Along with this line, we emphasize that the SO(4) symmetry is the lowest group-symmetry that enables us to investigate superconductivity and antiferromagnetism on an equal footing. We have imposed this by decomposing the electron operator into auxiliary fermionic and slave-boson constituents that respect SU(2)$_{rm spin}otimes$SU(2)$_{eta{rm spin}}$. This is used not in a mean-field treatment as in the usual slave-boson formalisms, but instead in the DMFT impurity solver with an SU(2)$_{rm spin}otimes$SU(2)$_{eta{rm spin}}$ hybridization function to incorporate the FLEX-generated bath information into DMFT iterations. While there have been attempts such as the doublon-less SU(2) slave-boson formalism, the present full-SU(2) slave-boson formalism is expected to provide a new platform for addressing the underlying physics for various quantum orders, which compete with each other and can coexist.
Using a dynamical cluster quantum Monte Carlo approximation we investigate the d-wave superconducting transition temperature $T_c$ in the doped 2D repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings $tp$ and $t$ in the form of a checkerboard pattern where $t$ is the hopping within a $2times2$ plaquette and $tp$ is the hopping between the plaquettes. We find inhomogeneity suppresses $T_c$. The characteristic spin excitation energy and the strength of d-wave pairing interaction decrease with decreasing $T_c$ suggesting a strong correlation between these quantities.
We present in this work an exact renormalization group (RG) treatment of a one-dimensional $p$-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a $p$-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining $p$-wave superconductivity in a one-dimensional system without spin-orbit interaction.
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