The Dynamic Hubbard Model (DHM) has been introduced as a framework for the electron-hole asymmetry observed in materials like high-temperature superconductors. In this study, we aim to understand the intricate dynamics of hole interactions, particularly focusing on the competition between on-site repulsion and hole-lattice coupling. Our results reveal a striking feature-an effective nearest-neighbor attraction between holes, even in the presence of the on-site repulsion typical of Mott insulators. Notably, the on-site repulsion not only coexists but also enhances the nearest-neighbor coupling. Our exploration of the DHM unravels unexpected and significant characteristics, enriching our understanding of hole interactions in correlated electron systems. The model's capacity to capture both on-site repulsion and effective nearest-neighbor attraction offers a valuable perspective.
The Dynamic Hubbard Model (DHM) has been introduced as a framework for the electron-hole asymmetry observed in materials like high-temperature superconductors. In this study, we aim to understand the intricate dynamics of hole interactions, particularly focusing on the competition between on-site repulsion and hole-lattice coupling. Our results reveal a striking feature-an effective nearest-neighbor attraction between holes, even in the presence of the on-site repulsion typical of Mott insulators. Notably, the on-site repulsion not only coexists but also enhances the nearest-neighbor coupling. Our exploration of the DHM unravels unexpected and significant characteristics, enriching our understanding of hole interactions in correlated electron systems. The model's capacity to capture both on-site repulsion and effective nearest-neighbor attraction offers a valuable perspective.
The conventional, single band Hubbard model captures the dynamics that arise in strongly correlated electron systems in the competition between electron transport and local Coulomb interactions. However, some of the important physics of real lattices is overlooked by its simplicity. The dynamic Hubbard model (DHM) provides additional degrees of freedom for electron states in a lattice by including a higher energy orbital and hybridization parameters for electrons to take advantage of a reduced Coulomb repulsion in the upper orbital when the lattice is at half-filling. This ``relaxation'' of the electronic state is accompanied by an asymmetry between electron and hole quasiparticles in the model. In this thesis we employ the computational tool of multiorbital dynamical mean field theory (MODMFT) to study electron-hole asymmetry in the DHM as evidenced in the behaviour of the quasiparticle weight and optical conductivity of electrons. In agreement with previous exact diagonalization work on the DHM, we find that the relaxation of electronic states is associated with quasiparticle dressing in the hole regime of the lower orbital, and a transfer of optical conductivity spectral weight from low to high frequencies. These observations are evidences of the electron-hole asymmetry in the two-orbital system. In this context, we evaluate the role of two critical variables in the DHM: the local and nonlocal hybridizations which parameterize interorbital electron transitions in the Hamiltonian. We demonstrate that the electron-hole asymmetry of the model has a more complex relationship to these hybridization parameters than previously identified. Mott physics plays an essential role in the quasiparticle dressing due to the local hybridization, while the nonlocal hybridization promotes electron-hole asymmetry by providing a separate channel for electron transport which serves to reduce the quasiparticle weight of holes in the lower band. We also briefly examine the phenomenon of orbital selective Mott transitions in the DHM within the parameter regime of electron state relaxation, and evaluate the role played by the hybridization parameters in this context.
The Hubbard and related models serve as a fundamental starting point in understanding the novel experimental phenomena in correlated electron materials, such as superconductivity, Mott insulator, magnetism. Recent numerical simulations demonstrate that the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a key role for the superconductivity. However, the impacts of long-range intersite interactions in such a ${t}^{\ensuremath{'}}$-Hubbard model are less explored. Using the state-of-art density-matrix renormalization group method, we investigate the ${t}^{\ensuremath{'}}$-Hubbard model on a two-leg ladder with the intersite interactions extended to the fourth neighbors. The numerical results show that the quasi-long-range superconducting correlation remains stable under the repulsive intersite interactions and these long-range repulsive interactions only change the ground state quantitatively. In addition, inspired by recent experiments on one-dimensional cuprate chain ${\mathrm{Ba}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$, we find that the nearest-neighbor attractive interaction significantly enhances the superconducting correlation when it is comparable to the nearest-neighbor hopping t. Stronger attraction drives the system into an electron-hole phase separation. Finally, we discuss the effects of the on-site interaction on superconductivity.
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.
High temperature superconductivity in copper oxides (cuprates) represents one of the most striking phenomena in condensed matter physics. These materials host superconducting states with the highest known critical temperatures, emerging upon doping antiferromagnetic insulator compounds. The antiferromagnetic (AF) insulating and superconducting (SC) phases defy standard descriptions in terms of band picture and conventional phonon-mediated superconductivity. In fact, these phenomena are genuine signatures of strong electronic correlations which hinder effective single-particle descriptions of the many-electron system. After 40 years since their discovery, it is widely accepted that the Hubbard model on the square lattice provides a minimal description of the low-energy electronic properties of cuprates. The model describes the competition between the electronic kinetic energy, modelled by nearest-neighbours hopping t, and the Coulomb repulsion, modelled by a purely local interaction potential U. At half-filling, this competition results in the so-called "Mott localisation" phenomenon, which distinguishes the metallic phase for U/t « 1 from an insulating phase for U/t » 1. The latter is characterised by the almost complete localisation of electrons due to the high energetic cost of hopping towards occupied sites. Interestingly, this basic competition is intimately related to AF ordering and, upon doping, to the formation of the SC state with characteristic d-wave symmetry. The fact that a purely repulsive interaction U is responsible for the formation of a SC state is remarkable, being superconductivity typically associated with an effective attractive interaction. In fact, a d-wave SC state can also be obtained, in general, by considering an attractive potential between electrons of neighbouring sites. Motivated by this observation, in this thesis, we study a modified version of the Hubbard model, dubbed as the "extended Hubbard model", in which we include a nearest-neighbours attractive potential -V. The general goal of this work is to explore the interplay between the purely local repulsion and the non-local attraction. This is not only motivated by the fact that both interactions are, in principle, responsible for d-wave superconductivity, but also by recent experimental observations which strongly suggest that the term -V needs to be included in order to accurately describe the magnetic spectra of some specific compounds. In this thesis, we study the extended Hubbard model using the Hartree-Fock method. Namely, we approximate the ground state by implementing a variational search in the subspace of the many-body Hilbert space of gaussian states. Despite its simplicity, the Hartree-Fock method provides a powerful framework to study competition among different phases, originating from different symmetry breaking mechanisms. In particular, we study the competition between three different phases: the normal phase, characterised by no symmetry breaking, the AF phase, characterised by a lowering of SU(2) symmetry, and the SC phase, characterised by the breaking of U(1) charge conservation. This thesis work led to a number of original results, which can be summarised by the general observation that the non-local attraction -V acts cooperatively with the local repulsion U for the stabilisation of the various phases hosted by the Hubbard model. For the normal phase, we find that the non-local attraction acts as a source of Mott localisation, leading to an effective reduction of the electronic bandwidth. In particular, for values of V larger than a critical value and close to half-filling, we find a strong Mott localisation characterised by the complete flattening of the electronic bands. Interestingly, this result shows an example of Mott localisation that can be described at the level of the Hartree-Fock approximation, whereas Mott localisation in the conventional Hubbard model usually requires more sophisticated approximation schemes. For the AF phase, we restrict our analysis to the half-filled case. We find that the pairing-induced Mott localisation leads to a significant enhancement of the magnetisation, primarily originating from the local repulsion U. Finally, we focus on the superconducting phase and derive self-consistency equations in both singlet and triplet Cooper pairing channels, showing how Cooper pairing can be mediated simultaneously by both the local repulsion and the non-local attraction. Therefore, we numerically investigate the singlet channel and find evidence of "symmetry mixing", namely, the formation of a superconducting gap that is neither symmetric nor anti-symmetric under rotations of π/2 in the plane. We show that symmetry mixing is connected to the emergence of a finite nematic order parameter, that signals the breaking of planar rotational symmetry. This nematic symmetry breaking results in the fact that the renormalisation of bands becomes anisotropic, producing a difference in electronic kinetics in the x and y directions. To summarise, the original results obtained in this thesis show that the non-local pairing provides a different route towards the formation of key strongly correlated phenomena, including Mott localisation and nematic superconductivity, and call for future investigation using more sophisticated methods such as, for example, the Dynamical Mean Field Theory.
Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and d-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The d-wave order parameter is found to scale like the superexchange coupling J for on-site interaction U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping ${t}^{\ensuremath{'}}$, the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping ${t}^{\ensuremath{''}}$ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs Tc∕Tcmax phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling, d-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.
We study a two-orbital attractive Hubbard model with a repulsive Hund's exchange coupling J as an idealized model for a two-band superconductor. This framework is motivated by a system where a large isotropic electron-phonon coupling drives the on-site Hubbard repulsion U negative, while leaving the exchange term unaffected. We focus on the intra-orbital (intra-band) singlet superconducting phase and we solve the model at zero temperature and half-filling using Dynamical Mean-Field Theory. Already at J=0, the two-orbital model features a superconductor-insulator transition as ∣U∣ grows, as opposed to the single-orbital case which remains superconducting for any U<0. We find that a finite J strengthens the effect of the attractive U, both in the normal state and, more significantly, in the superconducting state. However, this pushes the system towards an effectively stronger coupling, hence to a faster transition to the insulating state. Remarkably, the transition from a superconductor to an insulator occurs with a vanishing quasi-particle weight Z and in a scenario that recalls strongly correlated superconductivity close to a Mott transition, even though the present model is dominated by attractive interactions.