We carry out a detailed numerical study of the three-band Hubbard model in the underdoped region both in the hole- as well as in the electron-doped case by means of the variational cluster approach. Both the phase diagram and the low-energy single-particle spectrum are very similar to recent results for the single-band Hubbard model with next-nearest-neighbor hoppings. In particular, we obtain a mixed antiferromagnetic+superconducting phase at low doping with a first-order transition to a pure superconducting phase accompanied by phase separation. In the single-particle spectrum a clear Zhang-Rice singlet band with an incoherent and a coherent part can be seen, in which holes enter upon doping around $(π/2,π/2)$. The latter is very similar to the coherent quasi-particle band crossing the Fermi surface in the single-band model. Doped electrons go instead into the upper Hubbard band, first filling the regions of the Brillouin zone around $(π,0)$. This fact can be related to the enhanced robustness of the antiferromagnetic phase as a function of electron doping compared to hole doping.
We use quantum Monte Carlo methods and single-mode approximation to study the magnon dispersion in the 2D half-filled Hubbard and phonon-coupled Heisenberg models. We find that in the Hubbard model with $U/t< 8$, high-energy magnon dispersion is similar to those observed in inelastic neutron scattering experiments in ${La}_2{CuO}_4$. On the other hand, our studies of a 2D Heisenberg model coupled to dynamic optical bond phonons, fails to reproduce the experimental dispersion. These results can be interpreted as evidence for intermediate $U/t$ and charge fluctuations in the cuprate materials.
In this paper, from the microscopic Hubbard Hamiltonian we extract the local spin-singlet amplitude due to short-range spin correlations, and quantify its strength near half-filling. As a first application of the present approach, we study a problem of the energy dispersion and its d-wave modulation in the insulating cuprates, Sr$_{2}$CuO$_{2}$Cl$_{2}$ and Ca$_{2}$CuO$_{2}$Cl$_{2}$. Without any adjustable parameters, most puzzling issues are naturally and quantitatively explained within the present approach.
We study a 3-band extended Hubbard model on a CuO_3 system by the density matrix renormalization group (DMRG) method. Our system has geometry similar to that of a section of the CuO_2 plane of the copper-oxide superconductors. We have studied the effects of nearest-neighbour repulsions on the current-current correlations of two model CuO_3 systems. We show that repulsive interactions are clearly capable of increasing the magnitude of the current-current correlations in both models studied. The long-distance behavior of the current-current correlations is qualitatively influenced by V. We show …
Friedel oscillations induced by open boundary conditions in a two-band Hubbard model for CuO chains are numerically studied. We find that for physically realistic parameters and close to quarter filling, these oscillations have a 2k_F modulation according with experimental results on YBa_2Cu_3O_{7-delta}. In addition, we predict that, for the same parameters, as hole doping is reduced from quarter filling to half filling, Friedel oscillations would acquire a 4k_F modulation, typical of a strongly correlated electrons regime. The 4k_F modulation dominates also in the electron doped region. The …
While both the hole and electron doped cuprates can exhibit $d_{x^2-y^2}$-wave superconductivity, the local distribution of the doped carriers is known to be significantly different with the doped holes going primarily on the O sites while the doped electrons go on the Cu sites. Here we report the results of density matrix renormalization calculations for a three-orbital model of a CuO$_2$ lattice. In addition to the asymmetric dependence of the intra-unit-cell occupation of the Cu and O for hole and electron doping, we find important differences in the longer range spin and charge correlation…
We investigate the electron-energy loss spectrum of one-dimensional undoped CuO$_{3}$ chains within an extended multi-band Hubbard model and an extended one-band Hubbard model, using the standard Lanczos algorithm. Short-range intersite Coulomb interactions are explicitly included in these models, and long-range interactions are treated in random-phase approximation. The results for the multi-band model with standard parameter values agree very well with experimental spectra of Sr$_{2}$CuO$_{3}$. In particular, the width of the main structure is correctly reproduced for all values of momentum …
We study the electronic band-structure and transport properties of a CuO2-plane within the three-band Hubbard model. The Dynamical Mean-Field Theory (DMFT) is used to solve the many particle problem. The calculations show that the optical gap Delta_opt is given by excitations from the lower Hubbard band into the so called Zhang-Rice singlet band. The optical gap Delta_opt turns out to be considerably smaller than the charge transfer energy Delta (Delta=ep-ed) for a typical set of parameters, which is in agreement with experiment. For the two-dimensional CuO2-plane we investigated the dependenc…
The CuO-planes of high-T_c superconductors were found to consist of geometric stripes with alternating superconducting and antiferromagnetic areas. Here we will investigate the repulsive Hubbard model of striped clusters as a possible microscopic description of the superconducting elements. The focus of our attention lies on the superconducting properties. We report in agreement with the square Hubbard model a signal in the d-wave channel and investigate its dependence on system size, cluster shape and interaction strength.
We applied the Recurrent Variational Approach to the two-leg Hubbard ladder. At half-filling, our variational Ansatz was a generalization of the resonating valence bond state. At finite doping, hole pairs were allowed to move in the resonating valence bond background. The results obtained by the Recurrent Variational Approach were compared with results from Density Matrix Renormalization Group.
The spectral-weight distribution in recent neutron scattering experiments on the parent compound La$_2$CuO$_4$ (LCO), which are limited in energy range to about 450\,meV, is studied in the framework of the Hubbard model on the square lattice with effective nearest-neighbor transfer integral $t$ and on-site repulsion $U$. Our study combines a number of numerical and theoretical approaches, including, in addition to standard treatments, density matrix renormalization group calculations for Hubbard cylinders and a suitable spinon approach for the spin excitations. Our results confirm that the $U/…
Here we report results of a density-matrix-renormalization-group (DMRG) calculation of the charge, spin, and pairing properties of a two-leg CuO Hubbard ladder. The outer oxygen atoms as well as the rung and leg oxygen atoms are included along with near-neighbor and oxygen-hopping matrix elements. This system allows us to study the effects of hole and electron doping on a system which is a charge transfer insulator at a filling of one hole per Cu and exhibits power law, d-wave-like pairing correlations when doped. In particular, we focus on the differences between doping with holes or electron…
In a recent Letter, Peets, et al. measured the x-ray intensity at the oxygen K-edge in overdoped La$_{2-x}$Sr$_x$CuO$_{4\pmδ}$ (LSCO) and Tl$_2$Ba$_2$CuO$_{6+δ}$. They claimed that, unlike the underdoped samples of LSCO and YBa$_2$Cu$_3$O$_x$ in which the integrated intensity increases at least linearly with doping, it saturates abruptly for a hole count exceeding $x\approx 0.23$. They interpreted the saturation as a breakdown of the 1-band Hubbard model in the cuprates. However, we show that their results are in quantitative agreement with the 1-band Hubbard model.
A variational ground state of the repulsive Hubbard model on a square lattice is investigated numerically for an intermediate coupling strength (U = 8t) and for moderate sizes (from 6 x 6 to 10 x 10). Our ansatz is clearly superior to other widely used variational wave functions. The results for order parameters and correlation functions provide new insight for the antiferromagnetic state at half filling as well as strong evidence for a superconducting phase away from half filling.
A trial wave function is proposed for studying the instability of the two-dimensional Hubbard model with respect to d-wave superconductivity. Double occupancy is reduced in a similar way as in previous variational studies, but in addition our wave function both enhances the delocalization of holes and induces a kinetic exchange between the electron spins. These refinements lead to a large energy gain, while the pairing appears to be weakly affected by the additional term in the variational wave function.
We compute dynamic spin susceptibilities in the two-dimensional Hubbard model using the method of Dual Fermions and provide comparison to lattice Monte Carlo and cluster dynamical mean field theory. We examine the energy dispersion identified by peaks in ${\rm Im}χ(ω,q)$ which define spin modes and compare the exchange scale and magnon dispersion to neutron experiments on the parent La$_2$CuO$_4$ cuprate. We present the evolution of the spin excitations as a function of Hubbard interaction strengths and doping and explore the particle-hole asymmetry of the spin excitations. We also study the c…
By making use of the self-consistent projection operator method with high-momentum and high-energy resolutions, we find a kink structure in the quasiparticle excitation spectrum of the two-dimensional Hubbard model in the underdoped regime. The kink is caused by a mixing between the quasiparticle state and excitations with short-range antiferromagnetic order. We suggest that this might be the origin of the strong concentration dependence of the 'kink' found in La_{2-x}Sr_{x}CuO_{4} (x=0.03-0.07).
The Fermi surface (FS) of an extended $d-p$ Hubbard model is investigated by a two-pole approximation in both situations with hole and electron doping. Using the factorization procedure proposed by Beenen and Edwards, superconductivity with singlet $d_{x^2-y^2}$-wave pairing is considered. The effects of the $d-p$ hybridization on the FS are the main focus in the present work. Nevertheless, the asymmetries between the hole- and electron-doped regimes and the effects of doping and Coulomb interaction on FS are also investigated. Particularly, it is shown that the crossover from hole-like to ele…
The canonical transformation diagonalizing the one-particle tight binding Hamiltonian for an alternating chain with two non-equivalent sites per unit cell has been used to introduce the Hubbard-like interactions (on-site, inter-site, bond-site and intra-bond) in the corresponding two-band model. The considerations have been restricted to the particular case, suggested by the undistorted 3/4-filled $CuO_{3}$ chain, where the alternating structure comes only from non-equal on-site atomic energies and the gap between the two bands is sufficiently large. The renormalization group method has been t…
We use angle-resolved photoemission spectroscopy to study the doping evolution of infinite-layer Sr$_{1-x}$La$_{x}$CuO$_{2}$ thin films grown by molecular-beam epitaxy. At low doping, the material exhibits a dispersive lower Hubbard band typical of the superconducting cuprate parent compounds. As carriers are added to the system, a continuous evolution from charge-transfer insulator to superconductor is observed, with the initial lower Hubbard band pinned well below the Fermi level and the development of a coherent low-energy band with electron doping. This two-component spectral function emph…
We use a mapping of the multiband Hubbard model for $CuO_{3}$ chains in $RBa_{2}Cu_{3}0_{6+x}$ (R=Y or a rare earth) onto a $t-J$ model and the description of the charge dynamics of the latter in terms pf s spinless model, to study the electronic structure of the chains. We briefly review results for the optical conductivity and we calculate the quantum phase diagram of quarter filled chains including Coulomb repulsion up to that between next-nearest-neighbor $Cu$ atoms $V_{2}$, using the resulting effective Hamiltonian, mapped onto an XXZ chain, and the method of crossing of excitation spectr…
Recent scanning tunneling spectroscopy experiments have provided evidence that dopant impurities in high- Tc superconductors can strongly modify the electronic structure of the CuO2 planes nearby, and possibly influence the pairing. To investigate this connection, we calculate the local magnetic superexchange J between Cu ions in the presence of dopants within the framework of the three-band Hubbard model, up to fifth-order in perturbation theory. We demonstrate that the sign of the change in J depends on the relative dopant-induced spatial variation of the atomic levels in the CuO2 plane, con…
In this paper we examine the effects of electron-hole asymmetry as a consequence of strong correlations on the electronic Raman scattering in the normal state of copper oxide high temperature superconductors. Using determinant quantum Monte Carlo simulations of the single-band Hubbard model, we construct the electronic Raman response from single particle Green's functions and explore the differences in the spectra for electron and hole doping away from half filling. The theoretical results are compared to new and existing Raman scattering experiments on hole-doped La$_{2-x}$Sr$_{x}$CuO$_{4}$ a…
Using a mapping from the three-band extended Hubbard model for cuprate superconductors into a generalized t-J model, and exact diagonalization of the latter in a 4x4 cluster, we determine the quasiparticle weight for destruction of a Cu or an O electrons with definite wave vector k. We also derive an approximate but accurate analytical expression which relates the O intensity with the quasiparticle weight in the generalized t-J model, and use it to obtain the O intensity from results of the self-consistent Born approximation. The k-dependence of Cu and O intensities is markedly different. In p…
We test the response to a threading magnetic field of rings of 5-site $C_{4v}$-symmetric repulsive Hubbard clusters connected by weak intercell links; each 5-site unit has the topology of a CuO$_{4}$ cluster and a repulsive interaction is included on every site. In a numerical study of the three-unit ring with 8 particles, we take advantage of a novel exact-diagonalization technique which can be generally applied to many-fermion problems. For O-O hopping we find Superconducting Flux Quantization (SFQ), but for purely Cu-Cu links bound pair propagation is hindered by symmetry. The results agree…
The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-$T_{\rm c}$ superconductors. In particular, the relationship between the number $n$ of CuO$_2$ layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature $T_{\rm c}^{\rm opt}$ is intriguing. As experimentally observed in layered cuprates, $T_{\rm c}^{\rm opt}$ increases when $n$ is increased, up to $n=3$, and, then, decreases for larger $n$. However, the mechanism behind the $n$ dependence of $T_{\r…
The electronic states near the Fermi level of recently discovered superconductor Ba$_2$CuO$_{4-δ}$ consist primarily of the Cu $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals. We investigate the electronic correlation effect and the orbital polarization of an effective two-orbital Hubbard model mimicking the low-energy physics of Ba$_2$CuO$_{4-δ}$ in the hole-rich regime by utilizing the dynamical mean-field theory with the Lanczos method as the impurity solver. We find that the hole-overdoped Ba$_2$CuO$_{4-δ}$ with $3d^8$ (Cu$^{3+}$) is in the orbital-selective Mott phase (OSMP) at half-filling, an…
A novel hybrid scheme is proposed. The {\it ab initio} LDA calculation is used to construct the Wannier functions and obtain single electron and Coulomb parameters of the multiband Hubbard-type model. In strong correlation regime the electronic structure within multiband Hubbard model is calculated by the Generalized Tight-Binding (GTB) method, that combines the exact diagonalization of the model Hamiltonian for a small cluster (unit cell) with perturbation treatment of the intercluster hopping and interactions. For undoped La$_2$CuO$_4$ and Nd$_2$CuO$_4$ this scheme results in charge transfer…
Variational Monte Carlo study of a two-orbital Hubbard model for the iron pnictides
International School for Advanced Studies (SISSA) and CNR-IOM（国际高等研究院（SISSA）与意大利国家研究委员会凝聚态物理研究所（CNR-IOM））；Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino（都灵理工大学DISAT凝聚态物理与复杂系统研究所）
Using density matrix renormalization group calculations, we compare results obtained for the t-J, one-band Hubbard and three-band Hubbard models of a two-leg CuO ladder. Spin and charge gaps, pair binding energies, and effective pair hoppings are calculated for a wide range of parameters. All three models have an insulating state at a filling corresponding to one hole per Cu site. For physically relevant parameters their spin gaps are similar in size but they exhibit quite different charge gaps. We find that the binding energy of a pair of doped holes is of the order of the undoped ladder spin…
We study superconductivity in two-band models where one of the bands does or does not intersect the Fermi level depending on the parameter values. Applying a many-variable variational Monte-Carlo method for a Hubbard model on two-leg ladder and bilayer square lattices, we show that superconductivity can be enhanced in a parameter regime where the edge of one of the bands is near the Fermi energy, that is, when the band is incipient. The resemblence of the present results to those obtained by a weak coupling method in a recent study suggests that, even in the large $U$ regime, the suppression o…
We explore the effect of local charge fluctuations on the spin response of a Mott insulator by deriving an effective spin model, and studying it using Schwinger boson mean field theory. Applying this to La$_2$CuO$_4$, we show that an accurate fit to the magnon dispersion relation, measured by Coldea {\em et al.} [Phys. Rev. Lett. {\bf 86}, 5377 (2001)] is obtained with Hubbard model parameters $U \approx 2.34 eV$, and $t \approx 360 meV$. These parameters lead to estimates of the staggered magnetization ($m_s \approx 0.25$), spin wave velocity ($c\approx 800 meV$-Å), and spin stiffness ($ρ_s \…
Using the variational cluster approach based on the self-energy functional theory, we study the possible occurrence of excitonic order and superconductivity in the two-orbital Hubbard model with intra- and inter-orbital Coulomb interactions. It is known that an antiferromagnetic Mott insulator state appears in the regime of strong intra-orbital interaction, a band insulator state appears in the regime of strong inter-orbital interaction, and an excitonic insulator state appears between them. In addition to these states, we find that the $s^{\pm}$-wave superconducting state appears in the small…
The next-nearest-neighbour hopping term t' is shown to stabilize the AF state of the doped Hubbard model with respect to transverse perturbations in the order- parameter by strongly suppressing the intraband particle-hole processes. For a fixed sign of t', this stabilization is found to be significantly different for electron and hole doping, which qualitatively explains the observed difference in the degree of robustness of the AF state in the electron-doped (Nd_{2-x}Ce_{x}CuO_{4}) and hole-doped (La_{2-x}Sr_{x}CuO_{4}) cuprates. The t'-U phase diagram is obtained for both signs of the t' ter…
Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here we focus on variational approaches, but comparisons with both Quantum Cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferroma…
We present a joint experimental and theoretical study of the electronic structure of the cuprate chain systems A_(1-x)CuO_2 (A=Ca,Sr,Ba), as measured using O-K and Cu-L_3 x-ray absorption spectroscopy. The doping-dependent behaviour in these systems is radically different to that in conventional 2D cuprate networks formed from corner sharing CuO_4 plaquettes, and follows from the strongly suppressed inter-plaquette hybridisation resulting from the 90 degree Cu-O-Cu interaction pathway in the chain systems. Spectroscopically, this results in (a) a classical mixed-valent scenario whereby the dif…
We perform a variational Monte Carlo study on spontaneous d-wave form Fermi surface deformation ($d$FSD) within the three-band Hubbard model. It is found that the variational energy of a projected Fermi sea is lowered by introducing an anisotropy between the hopping integrals along the x and y directions. Our results show that the $d$FSD state has the strongest tendency at half-filling in the absence of magnetism, and disappears as the hole concentration increases to $n_h\approx 1.15$. This is qualitatively in agreement with the mean field analysis and the exact diagonalization calculation for…
The recently discovered cuprate superconductor Ba$_2$CuO$_{3+δ}$ exhibits a high $T_c\simeq73$K at $δ\simeq0.2$. The polycrystal grown under high pressure has a structure similar to La$_2$CuO$_4$, but with dramatically different lattice parameters due to the CuO$_6$ octahedron compression. The crystal field in the compressed Ba$_2$CuO$_4$ leads to an inverted Cu $3d$ $e_g$ complex with the $d_{x^2-y^2}$ orbital sitting below the $d_{3z^2-r^2}$ and an electronic structure highly unusual compared to the conventional cuprates. We construct a two-orbital Hubbard model for the Cu $d^9$ state at hol…
We study current-current correlations in the three-band Hubbard model for two-leg CuO ladders using the density-matrix renormalization group method. We find that these correlations decrease exponentially with distance for low doping but as a power law for higher doping. Their pattern is compatible with the circulating current (CC) phase which Varma has proposed to explain the pseudo-gaped metallic phase in underdoped high-temperature superconductors. However, for model parameters leading to a realistic ground state in the undoped ladder, the current fluctuations decay faster than the d-wave-li…
We have performed angle-resolved photoemission and core-level x-ray photoemission studies of the single-layer cuprate Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+δ}$ (Bi2201) and revealed the doping evolution of the electronic structure from the lightly-doped to optimally-doped regions. We have observed the formation of the dispersive quasi-particle band, evolution of the Fermi ``arc'' into the Fermi surface and the shift of the chemical potential with hole doping as in other cuprates. The doping evolution in Bi2201 is similar to that in Ca$_{2-x}$Na$_{x}$CuO$_{2}$Cl$_2$ (Na-CCOC), where a rapid chemical po…
Normal states of the attractive Hubbard model, especially in two dimension, are studied in the light of a transition from a Fermi liquid to an insulating or gapped state. A series of variational Monte Carlo calculations with better statistics is carried out to estimate accurately expectation values by several many-body wave functions. Although a relatively clear crossover is observed even in the plain Gutzwiller wave function, the states in both regimes are metallic. Meanwhile, a substantial metal-insulator transition takes place at |U|\sim W (band width) in an improved wave function in which …
The density-matrix renormalization-group method is used to study the electronic states of a two-chain Hubbard model for CuO double chains of PrBa$_2$Cu$_4$O$_8$. We show that the model at quarter filling has the charge ordered phases with stripe-type and in-line--type patterns in the parameter space, and in-between, there appears a wide region of vanishing charge gap; the latter phase is characteristic of either Tomonaga-Luttinger liquid or a metallic state with a spin gap. We argue that the low-energy electronic state of the CuO double chains of PrBa$_2$Cu$_4$O$_8$ should be in the metallic s…
A microscopic theory for electronic spectrum of the CuO2 plane within an effective p-d Hubbard model is proposed. Dyson equation for the one-electron Green function in terms of the Hubbard operators is derived which is solved self-consistently for the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by kinematical interaction is described by a model dynamical spin susceptibility. Doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface and the coupling constant are studied.
We use the variational cluster approximation to study the superconducting ground state in the two-dimensional attractive Hubbard model, putting particular emphasis on the significance of quantum fluctuations of the system. We first show that the order parameter is suppressed in comparison with that obtained using the mean-field theory owing to the effects of spatial fluctuations in two-dimensional systems. We then show that the calculated Bogoliubov quasiparticle spectra and condensation amplitude clearly exhibit the character of Cooper pairs in momentum space and that the pair coherence lengt…
Using the variational cluster approach (VCA), we study the transition from the antiferromagnetic to the superconducting phase of the two-dimensional Hubbard model at zero temperature. Our calculations are based on a new method to evaluate the VCA grand potential which employs a modified Lanczos algorithm and avoids integrations over the real or imaginary frequency axis. Thereby, very accurate results are possible for cluster sizes not accessible to full diagonalization. This is important for an improved treatment of short-range correlations, including correlations between Cooper pairs in parti…
Using an exact diagonalization method within the dynamical mean-field theory we study stripe phases in the two-dimensional Hubbard model. We find a crossover at doping $δ\simeq 0.05$ from diagonal stripes to vertical site-centered stripes with populated domain walls, stable in a broad range of doping, $0.05<δ<0.17$. The calculated chemical potential shift $\propto -δ^2$ and the doping dependence of the magnetic incommensurability are in quantitative agreement with the experimental results for doped La$_{2-x}$Sr$_x$CuO$_4$. The electronic structure shows one-dimensional metallic behavior along …
We study the correlation-induced deformation of Fermi surfaces by means of a new diagrammatic method which allows for the analytical evaluation of Gutzwiller wave functions in finite dimensions. In agreement with renormalization-group results we find Pomeranchuk instabilities in two-dimensional Hubbard models for sufficiently large Coulomb interactions.
We develop a diagrammatic method for the evaluation of general multi-band Gutzwiller wave functions in finite dimensions. Our approach provides a systematic improvement of the widely used Gutzwiller approximation. As a first application we investigate itinerant ferromagnetism and correlation-induced deformations of the Fermi surface for a two-band Hubbard model on a square lattice.
We use the Gutzwiller variational many-body theory to investigate the stability of orbitally ordered states in a two-band Hubbard-model without spin degrees of freedom. Our results differ significantly from earlier Hartree-Fock calculations for this model. The Hartree-Fock phase diagram displays a large variety of orbital orders. In contrast, in the Gutzwiller approach orbital order only appears for densities in a narrow region around half filling.
We develop the variational-cluster-approximation method based on the thermal-pure-quantum-state approach and apply the method to the calculations of the thermodynamic properties of the Hubbard model, thereby obtaining the temperature dependence of the single-particle excitation spectra, entropy and specific heat, and order parameter of the antiferromagnetic phase efficiently. We thus demonstrate that the method developed here has a potential power for elucidating finite-temperature properties of strongly correlated electron systems.
We investigate the electronic and superconducting properties of a negative-U Hubbard model. For this purpose we evaluate a recently introduced variational theory based on Gutzwiller-correlated BCS wave functions. We find significant differences between our approach and standard BCS theory, especially for the superconducting gap. For small values of $|U|$, we derive analytical expressions for the order parameter and the superconducting gap which we compare to exact results from perturbation theory.
We use the $C_{4v}$ symmetry group of the 4-site Hubbard model to construct a ground state variational wave function of two- and four interacting electrons. In the limit $U\rightarrow 0$, ground state energies of the two- and four interacting electrons system is of the order $-4t$. The variational wave function of the four interacting electrons obtained using the $B_1$ irreducible representation is valid for on-site Coulomb repulsion, while the one obtained using the $A_1$ representation is valid for negative values of the Coulomb interaction. The system exhibits antiferromagnetic correlations…
We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$, where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulo…
We show how an accurate first-principles treatment of the antiferromagnetic (AFM) ground state of La$_2$CuO$_4$ can be obtained without invoking any free parameters such as the Hubbard $U$. The magnitude and orientation of our theoretically predicted magnetic moment of $0.495 μ_{B}$ on Cu-sites along the (100) direction are in excellent accord with experimental results. The computed values of the band gap (1.00 eV) and the exchange-coupling (-138 meV) match the corresponding experimental values. We identify interesting band splittings below the Fermi energy, including an appreciable Hund's spl…
We investigate the electronic and structural properties of CuO, which shows significant deviations from the trends obeyed by other transition-metal monoxides. Using an extended Hubbard corrective functional, we uncover an orbitally ordered insulating ground state for the cubic phase of this material, which was expected but never found before. This insulating state results from a fine balance between the tendency of Cu to complete its d-shell and Hund's rule magnetism. Starting from the ground state for the cubic phase, we also study tetragonal distortions of the unit cell (recently reported in…
