Understanding competing instabilities in systems with correlated fermions remains one of the holy grails of modern condensed matter physics. Among the fermionic lattice models used to this effect, the extended Hubbard model occupies a prime place due to the potential relevance of its repulsive and attractive versions for both electronic materials and artificial systems. Using the recently introduced multichannel fluctuating field approach, we address the interplay of fluctuations in the charge density wave, $s$-wave superconducting, and phase separation channels in the attractive extended Hubbard model. Despite the fact that this model has been intensively studied for decades, our approach allows us to identify a phase that has not been analyzed before and which is characterized by the coexistence of collective $s$-wave superconducting and phase separation fluctuations. Our findings resonate with previous observations of interplaying phase separation and superconducting phases in electronic systems, most importantly in high-temperature superconductors.
Understanding competing instabilities in systems with correlated fermions remains one of the holy grails of modern condensed matter physics. Among the fermionic lattice models used to this effect, the extended Hubbard model occupies a prime place due to the potential relevance of its repulsive and attractive versions for both electronic materials and artificial systems. Using the recently introduced multichannel fluctuating field approach, we address the interplay of fluctuations in the charge density wave, s-wave superconducting, and phase separation channels in the attractive extended Hubbard model. Despite the fact that this model has been intensively studied for decades, our approach allows us to identify a phase that has not been analyzed before and which is characterized by the coexistence of collective s-wave superconducting and phase separation fluctuations. Our findings resonate with previous observations of interplaying phase separation and superconducting phases in electronic systems, most importantly in high-temperature superconductors.
Strongly correlated systems often display rich phase diagrams exhibiting different ordered phases involving spin, charge, pairing, or orbital degrees of freedom. The theoretical description of the competition between different instabilities in strongly correlated systems giving rise to this phenomenology, remains one of the holy grails of modern condensed matter theory. It poses a tremendous challenge of both conceptual and computational complexity, and thus the interplay of competing electronic fluctuations constitutes a roadblock to the understanding of the complex phase diagrams of a wide range of correlated quantum materials. This motivates the search for constructing simplified methods to study interplaying collective fluctuations.We introduce a multichannel extension of the recently developed fluctuating field approach to competing collective fluctuations in correlated electron systems. The method is based on a variational optimization of a trial action that explicitly contains the order parameters of the leading fluctuation channels. It gives direct access to the free energy of the system, facilitating the distinction between stable and metastable phases of the system.We apply our approach to the extended Hubbard model, a paradigmatic fermionic lattice model, occupying a prime place in condensed matter theory due to the potential relevance of its repulsive and attractive versions for both electronic materials and artificial systems.Utilising the technique to study the weak to intermediate coupling regime of the repulsive interaction, we find it to capture the interplay of competing charge density wave and antiferromagnetic fluctuations with qualitative agreement with more computationally expensive methods. In addition, the method allows access to excited-state properties, through the one-particle excitation spectrum, and many-body correlation effects, through the self-energy, directly on the real-frequency axis without using numerical analytic continuation techniques. The multichannel fluctuating field approach thus offers a promising route for a numerically low-cost treatment of the interplay between collective fluctuations in small to large systems.Using the introduced multichannel fluctuating field approach, we explore the phase diagram of the extended Hubbard model in both repulsive and attractive regimes, addressing the interplay of fluctuations in the antiferromagnetic, charge density wave, s-wave superconducting, and phase separation channels. Despite the fact that this model has been intensively studied for decades, our novel approach allows us to identify a novel phase that is characterised by the coexistence of collective s-wave superconducting and phase separation fluctuations. These findings resonate with previous observations of interplaying phase separation and superconducting phases in electronic systems, most importantly in high-temperature superconductors. In addition, the multichannel fluctuating field method allows to display the quintessential nature of the extended Hubbard model through the large variety of types of competitions which emerges from the interplaying instabilities. The general nature of the proposed theory, allowing to incorporate a variety of collective modes, makes it a promising tool for studying the interplay of collective fluctuations in strongly correlated fermionic systems.
The extended Hubbard model describes fermions on a lattice coupled through on-site, U, and first-neighbor, V, interactions. In the context of high-Tc cuprates, antiferromagnetic fluctuations may lead to an attractive channel, hence to superconductivity. Despite interest in the two-dimensional version of the model, the current knowledge about the phase diagram is still far from complete. Here, we report on the results of extensive determinant quantum Monte Carlo simulations for this model at half filling, in which we have used the average sign of the product of fermionic determinants as an additional observable to locate critical points. We arrive at a ground state phase diagram in the $U\text{\ensuremath{-}}V$ plane in which the boundaries involving antiferromagnetic, charge-ordered, s- and d-wave superconductivity, and phase-separated phases are quantitatively set with good accuracy. We have also proposed a partial phase diagram, Tc(U,V), featuring critical temperatures for the charge-density wave and s-wave superconducting phases.
Understanding superconductivity emerging from repulsive fermions remains a major challenge in condensed matter physics. In this paper, we investigate the pairing tendencies in a one-dimensional, three component repulsive Hubbard model, using the density matrix renormalization group method. At half-filling, the system exhibits density wave ground state due to strong Hubbard repulsions. Upon doping, we find that Cooper pairs can emerge, whose fluctuations predominate the long-range physics in the system across a wide parameter range. The effective attractions between Cooper pairs are mediated by the particle-hole fluctuations in the third non-pairing component, resembling an excitonic mechanism of superconductivity. The coexistence of multiple density waves and superconductivity at different fermion fillings is explored. We also present an analytical study of the pairing mechanism in both weak and strong coupling limits. Our results provide a new perspective for understanding and exploring unconventional superconductivities in strongly correlated fermionic systems.
We investigate the phase diagram of the extended Hubbard model on a half-filled honeycomb lattice through determinant quantum Monte Carlo simulations. At zero temperature, the repulsive Hubbard model undergoes a transition to an antiferromagnetic state only for sufficiently strong on-site coupling U. However, the inclusion of a repulsive extended interaction V between fermions in nearest-neighbor orbitals induces a charge-ordered phase. For attractive interactions, we also identify superconducting and phase-separated phases. We have determined a complete phase diagram with the aid of structure factors associated with various orderings, combined with measurements of double occupancy and the average sign of fermionic determinants. We have established that the semimetallic phase forms a zone from which ordered phases are excluded, preventing the stabilization of a superconducting phase with d-wave symmetry, i.e., only s-wave pairing is allowed.
The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and B2g (dxy) pairing dominates in the absence of repulsive longer-range Coulomb interactions VNN, the latter induces pairing in other symmetry channels, including, e.g., A2g (g-wave), nodal A1g (extended s-wave), or nodal Eu (p-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, VNN<0, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts Eu (p-wave) spin-triplet or B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.
Inhomogeneities on various length scales suggesting phase separation seem to be a generic feature of hole-doped high-temperature superconducting cuprates. Also firmly established is the d-wave symmetry of the superconducting state. The interplay of superconductivity and phase separation has been noted in previous mean-field studies of correlated electron models. To further explore this issue in a more rigorous approach we have conducted quantum Monte Carlo calculations of a two-dimensional Hubbard model with nearest-neighbor attractive interaction. For a vanishing on-site repulsion, the result agrees with that of Micnas, Ranninger, and Robaszkiewicz [Phys. Rev. B 39, 11 653 (1989)], and indicates that for a given strength of the attractive interaction, homogeneous d-wave superconducting phase can exist only above a critical doping concentration, below which phase separation occurs. A finite on-site repulsion modifies the phase separation behavior. A stronger d-wave pairing correlation is seen in the inhomogeneous phase compared to the homogeneous phase.