Hole pockets in the doped 2D Hubbard model

The electronic momentum distributionn(k) of the two dimensional Hubbard model is studied for different values of the couplingU/t, electronic density n, and temperature, using quantum Monte Carlo techniques. A detailed analysis of the data on 8 × 8 clusters shows that features consistent with hole pockets at momentak = (±/2,±/2) appear as the system is doped away from half-filling. Our results are consistent with recent experimental data for the cuprates discussed by Aebi et al. (Phys. Rev. Lett. 72, 5757 (1994)). In the range of couplings studied, the depth of the pockets is maximum at n 0.9,and it increases with decreasing temperature. The apparent absence of hole pockets in previous numerical studies of this model is explained.     

Shadow bands in models of correlated electrons

A consequence of strong antiferromagnetic correlations in models of high-Tc cuprates is the appearance in photoemission (PES) calculations of considerable more weight above the Fermi momentum PF than expected for non-interacting electrons. This effect, qualitatively discussed by Kampf and Schrieffer under the name of shadow bands, is here quantitatively analyzed in the two dimensional Hubbard and t-J models using Monte Carlo and exact diagonalization techniques in the realistic strong coupling regime.     

Anisotropic superconductivity in the two-dimensional Hubbard model

We address the problem of anisotropic superconductivity in the two-dimensional Hubbard model. The Eliashberg equations have been generalized to the case which accounts for the anisotropy of the order parameter. Strong local correlations are treated within the mean field slave boson approximation. The superconducting transition temperatureT _c is evaluated as a function of the occupation number. Our results indicate that thed-wave state is the most likely channel for superconductivity for small concentration of holes. We have also derived an approximate analytical formula forT _c valid for any value of the occupation number. In addition, the influence of strong correlations on the electron-phonon coupling function is also discussed.     

Interpolative approximation for the Hubbard and the emery model

Calculations in Green's function technique apply an interpolation ansatz for the self-energy between the weak and strong coupling regime to the doped case of correlated models. The DOS of the one-band Hubbard model with the Kondo-like peak at the chemical potential is in good agreement with recent numerical results. In the doped three-band model a singlet correlation band from copper and oxygen states appears at the Fermi surface with dispersion similar to the free bands but with strongly renormalized bandwidth. The Fermi surface changes from closed hole type to closed electron type upon doping and is perfectly nested for some doping valuen1.25.     

Two Domains of the Parameter Space of the 2D Hubbard Model for High-Tc Superconductors

High-T _c superconducting cuprates have two types of Fermi surfaces: simple-2D-tight-binding-band type (LSCO type) and the much deformed one (Bi2212 type). The difference is attributed to that of band parameter values, i.e., t′ ∼ −0.1 and t″ ∼ 0 versus t′ ∼ −0.3 and t″ ∼ 0.2 in terms of the second- and third-neighbor transfer energies t′ and t″, respectively (energy unit is the nearest-neighbor transfer energy t). Assuming a moderate value of on-site Coulomb energy U ∼ 6 and performing the variational Monte Carlo computation, we found that the two superconducting parameter domains exist in fact around these parameter sets, respectively, in which superconductivity predominates over spin density wave (SDW) due to the latter being at the brink of vanishing. Stripes were obtained in the first domain but tend to disappear in the second. In the latter domain there seems to exist parameter sets for which superconductivity appears without doping.     

Eliashberg equations with momentum-dependent Kernels for the two-dimensional Hubbard model

We discuss the impact of the strong electron-phonon interactions on the physical properties of correlated electrons in the two-dimensional Hubbard model. An easy access to the physical properties of the superconducting state is obtained by solving the Eliashberg equations with explicit momentum-dependent kernels. In order to facilitate the numerical procedure to solve these equations, correlations are treated within the Gutzwiller approximation (i.e., mean-field-slave boson approximation). Our results strongly support the view thatd-wave symmetry is the most important feature of the superconducting state in the copper oxides. A possible extension beyond the mean field approximation is also presented.Supported by the State Committee for Scientific Research, Grant No. 283021805.     

Cumulant calculations of thermodynamic quantities for the Hubbard and the emery model

The calculations of the first paper suggesting phase separation in the Hubbard model [2] are performed under modern computer facilties for the one and three-band Hubbard model. High-temperature approximations for specific heat and static correlation functions are obtained. The latter show, at these high temperatures, no tendency to phase separate in the same way as in the cited paper because our spin parallel nearest-neighbor charge correlation function is negative for all doping values. The spin antiparallel correlation function has positive and negative values for different doping regimes.Extension of this work to higher levels of iterations and to other correlation functions is in progress.     

Spectral functions for the 2D Hubbard model

Spectral functions and quasiparticle bands are calculated with the modified alloy analogy approximation and are found to be in excellent agreement with the Monte Carlo data of Bulut et al. The Fermi surfaces also agree and have anomalously large volumes for large U near half-filling. In the modified alloy analogy this is a symptom of the breakdown of Fermi liquid theory.We thank Dr. N. Bulut for communicating his results before publication and acknowledge the support of an SERC grant.     

Multiband superconductivity: A mapping to the extended attractive Hubbard model

Following our recent work which shows that purely repulsive multiband systems effectively reduce to the extended attractive Hubbard model having the on-site repulsion along with nearest-neighbor and next-nearst-neighbor attraction for the cuprate structures, we study the latter model in the mean-field theory.T _c against band filling for various symmetries of pairing is numerically calculated. The results show that, for the region of and expected for the mapping from the original multiband model,T _c has maximum values of the order of 100 K, which is consistent with the experimental results. For certain values of parameters,s- and -wave pairing have similar values of T_c, which may suggest the possibility of a mixed phase of the two.The numerical calculations were done on the HITAC S3800 in the University of Tokyo Computer Centre. This work was in part supported by a Grant-in-Aid from the Ministry of Education, Science, and Culture, Japan.     

D-Wave Superconductivity and Coulomb Correlations in the Two-Dimensional Hubbard Lattice

We considered anisotropic superconductivity within the two-dimensional Hubbard model extended by pairing correlations originating from the electron–phonon interaction. To discuss the onset of superconductivity close to the insulator–metal transition, we used the Hubbard I approximation to account for the formation of the insulating gap and see the role of Coulomb correlations for superconducting pairing. It has been shown that the Hubbard I approximation reflects effective pairing interactions genuine for correlated electron systems and leads to the stabilization of the superconductivity in the d-wave channel. One may expect the cooperation of phonon-free and phonon-induced mechanism in the formation of thed-wave superconducting state.     

s-Wave vs.d -Wave Superconductivity in the Two-Dimensional Hubbard Model

The anisotropic superconductivity has been considered in the two-dimensional Hubbard model. We allow for on and off-site intralayer Cooper pairs. Interlayer momentum-conserving Josephson tunneling which couples adjacent layers has been taken into account. The meanfield solution for the superconducting transition temperature demonstrates the competition between local Coulomb repulsion and interlayer tunneling in thes-wave channel. This competition leads to the mixedsd superconducting state at low doping. We also demonstrate thatc-phonon-assisted transitions between intra and interlayer states can effectively give rise to momentum-conserving Josephson tunneling.     

Effects of Higher Hopping Terms on the Stripe States in the Two-Dimensional Hubbard Model

Using the variational Monte Carlo method for the two-dimensional t-t′-t″-U Hubbard model, we discuss the ground state of the underdoped region on the high-T _c cuprates. We found that, while stripe states with the periodicity consistent with experiments for La_{2− x} Sr _x CuO₄ are stabilized in the case of t′/t < 0, the positive t′/t makes the stripe state unstable with the lowest energy state being the commensurate AF state, which is consistent with experiments on the electron doping system such as Nd_{2− x} Ce _x CuO₄. We also show that the stripe state is sensitive to the value of t″/t > 0. These results indicate that the nesting condition is a critical factor to the stripe instability.     

The Nagaoka instability and off-diagonal superconductivity in the finite Hubbard lattice

The first strict evidence for time-reversal symmetry breaking and change in statistics of electrons in U(1) gauge field, induced by periodic boundary conditions is demonstrated for ld Hubbard model with U . The exact ground state energy, eigenfunction and one-particle density correlation function are calculated for arbitrary number of electrons and lattice sites. The criteria for the stability of either the Nagaoka state or spontaneously broken superconducting state with off-diagonal long-range order are found. The theory predicts the existence of superconductivity and ferromagnetism for electrons in periodic lattices and mesoscopic rings. The electrons in lattices are shown to provide for the presence of parity-dependent paramagnetic and diamagnetic persistent currents in the ground state.     

Some results from quantum monte carlo studies of the 2D Hubbard model

Quantum Monte Carlo calculations have provided insights into the magnetic, single-particle, and effective particle-particle interaction in the two-dimensional Hubbard model. Here we review some of these results.     

Thermodynamics of the Frustrated 2D Hubbard Model

The thermodynamic properties of the quarter filled 2D Hubbard model extended by next-nearest-neighbor (NNN) hopping have been studied in an exact diagonalization method on a tilted square cluster. The NNN hopping interaction (i.e. frustration) is prominent at the low-temperature region. A positive (negative) diagonal hopping t′ favors (suppresses) double occupancy and hence decreases (increases) local moment. At higher temperatures thermal excitations favor the formation of doublans against the strong Coulomb repulsion U and the weak diagonal hopping, hence decreasing local moment. A two-peak structure is observed in the specific heat curves with the inclusion of negative NNN hopping. The low-T peak in specific heat is highly suppressed in comparison to the high-T peak. It has also been argued that t′ influences the ‘pseudogap’ energy scale. In the present case of quarter filling, a weak and short range antiferromagnetic order is present at very low temperatures, which is slightly suppressed (enhanced) by positive (negative) t′. The effect of t′ is more pronounced in the non-interacting limit.     

An exact study of pairing fluctuations and phase diagrams in four-site Hubbard Nanoclusters

Charge-spin separation and pairing fluctuations and pseudogaps are studied using the analytical eigenvalues of the four-site Hubbard Nanoclusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature (T), magnetic field (h), on-site interaction (U), chemical potential (μ), and number of electrons (N). The electron charge energy gap, with one hole off half filling, corresponds to an excitonic particle–hole pair binding energy Δ ^e-h > 0 at U > U _c and vanishes at a critical parameter U _c = 4.584. For U < U _c, particle–particle pair binding is found with a pairing energy Δ^p > 0. In addition, for U ⩽ U _c we find an electron pair binding instability at finite temperature near N ≈ 3, which manifests a possible pairing mechanism, a precursor to superconductivity, in small clusters. The resulting phase diagram, consisting of charge and spin pseudogaps, hole pairing near 1/8th filling with hole-rich and hole-poor regions in the ensemble of Nanoclusters, closely resembles the phase diagrams in the family of doped high-T _c-cuprates.     

Superconductivity in the two-band hubbard model

We present a study of superconducting correlations in a two-band Hubbard model with a wide band strongly hybridized with a narrow band in which an attractive on-site interaction is operating. The narrow band pairs can induce superconducting correlations in the wide band through hybridization interaction. A generalized gap function for the induced wide-band pairing is obtained and its properties in the intermediate interaction region are analysed. Relevance of the results to high-T _c superconductors is briefly discussed.     

First-principles study on the electronic structure of Pb10-xCux(PO4)6O(x=0,1)

Recently,Lee et al.claimed the experimental discovery of room-temperature ambient-pressure super-conductivity in a Cu-doped lead-apatite(LK-99)(arXiv:2307.12008,arXiv:2307.12037).Remarkably,the claimed superconductivity can persist up to 400 K at ambient pressure.Despite the experimental im-plication,the electronic structure of LK-99 has not yet been studied.Here,we investigate the electronic structures of LK-99 and its parent compound using first-principles calculations,aiming to elucidate the doping effects of Cu.Our results reveal that the parent compound Pb10(PO4)6O is an insulator,while Cu doping induces an insulator-metal transition and thus volume contraction.The band structures of LK-99 around the Fermi level are featured by a half-filled flat band and a fully-occupied flat band.These two very flat bands arise from both the 2p orbitals of 1/4-occupied O atoms and the hybridization of the 3d orbitals of Cu with the 2p orbitals of its nearest-neighboring O atoms.Interestingly,we observe four van Hove singularities on these two flat bands.Furthermore,we show that the flat band structures can be tuned by including electronic correlation effects or by doping different elements.We find that among the considered doping elements(Ni,Cu,Zn,Ag,and Au),both Ni and Zn doping result in the gap opening,whereas Au exhibits doping effects more similar to Cu than Ag.Our work establishes a foundation for fu-ture studies to investigate the role of unique electronic structures of LK-99 in its claimed superconducting properties.     

Superconductivity in the cuprates as a consequence of antiferromagnetism and a large hole density of states

We briefly review a theory for the cuprates that has been recently proposed based on the movement and interaction of holes in antiferromagnetic (AF) backgrounds. A robust peak in the hole density of states (DOS) is crucial to produce a large critical temperature once a source of hole attraction is identified. The predictions of this scenario are compared with experiments. The stability of the calculations after modifying some of the original assumptions is addressed. We find that if the dispersion is changed from an antiferromagnetic band at half-filling to a tight-binding cosk _x+cosk _y narrow band at n=0.87, the main conclusions of the approach remain basically the same i.e., superconductivity appears in the -channel andT _c is enhanced by a large DOS. The main features distinguishing these ideas from more standard theories based on antiferromagnetic correlations are here discussed.     

A phenomenological theory for the spin-glass ordering in Fe doped YBa2Cu3O7+y

A phenomenological theory for spin-glass superconductor, based on a generalized Ginzburg-Landau free-energy functional d0epending on superconducting and spin-glass order parameters, is presented. It is found that the coupling between the superconducting and spin-glass order assists in freezing spins by enhancing the spin-glass order parameter but acts as a pair breaking effect for superconducting order by decreasing the superconducting order parameter. The schematic behavior of several thermodynamic quantities has been discussed. It is found that all these quantities show either cusps or discontinuities at the superconducting and/or spinglass transition temperatures.