The Hubbard model on a cube was revisited and extended by both nearest-neighbor (nn) Coulomb correlation and {nearest-neighbor} Heisenberg exchange. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on-site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossings in dependence on the various model parameters. Furthermore the groundstates of the pure Hubbard model in dependence on a magnetic field h coupled to the spins are shown for the complete U-h plane. For the cubic cluster gas we calculated the density $n(μ,T,h)$ and the thermodynamical density of states from the grand potential. The ground states and the various spin-spin correlation functions are studied for both attractive and repulsive values of the three interaction constants. The anomalous degeneration lines are calculated. For the cases where these lines end in triple points we give the related parameter values. The influence of the nn-exchange and the nn-Coulomb correlation onto the anomalous degeneration is discussed.
We investigate formation and condensation of fermion pairs in cold-atom quantum simulators for extended Hubbard models ($UV$ models) with body-centered-cubic (BCC) optical lattices in the dilute limit, predicting small and light pairs. Pair mass, radius, and binding conditions are calculated, and used to compute transition temperatures. We predict that: (a) local pairs form in BCC optical lattices and binding energies can be large; (b) for particular cases where onsite $U$ and intersite $V$ are attractive with similar size, pairs are both small and light; and (c) pairs of $^6$Li atoms Bose--Ei…
We study Hilbert space fragmentation in the extended Fermi-Hubbard model with nearest and next-nearest-neighbor interactions. Using a generalized spin/mover picture and saddle point methods, we derive lower bounds for the scaling of the number of frozen states and for the size of the largest block preserved under the dynamics. We find fragmentation for strong nearest- and next-nearest-neighbor repulsions as well as for the combined case. Our results suggest that the involvement of next-nearest-neighbor repulsions leads to an increased tendency for localization. We then model the dynamics for l…
Half-filled Hubbard Model on a Bethe lattice with next-nearest neighbor hopping
研究了具有最近邻和次最近邻跃迁$t_1$和$t_2$的Bethe晶格上Néel反铁磁性与顺磁金属-绝缘体跃迁（PMIT）之间的相互作用.我们在本文中集中在半填充的情况。对于$t_2/t_1\to 1$，PMIT超过反铁磁相，并显示出类似于V $_2$ O $_3$的情况。在这个参数制度，我们还观察到一个新的磁相。
We study the infinite-U Hubbard model on ladders of 2, 4 and 6 legs with nearest (t) and next-nearest (t') neighbor hoppings by means of the density-matrix renormalization group algorithm. In particular, we analyze the stability of the Nagaoka state for several values of t' when we vary the electron density $(ρ)$ from half-filling to the low-density limit. We build the two-dimensional phase diagram, where the fully spin-polarized and paramagnetic states prevail. We find that the inclusion of a non-frustrating next nearest neighbor hopping stabilizes the fully spin-polarized phase up until |t'/…
Nearest-Neighbor Repulsion and Competing Charge and Spin Order in the Extended Hubbard Model
我们推广了两粒子自洽方法（TPSC）来研究扩展的哈伯德模型，其中除了通常的局部屏蔽相互作用外，还存在最近邻相互作用。TPSC方法和Singwi Tosi Land Sjölander（STLS）近似的电子气之间的异同进行了讨论。通过与Y的量子蒙特卡罗计算的比较，我们的TPSC的扩展的准确性进行评估。Zhang和J.Callaway，\textbf{39}，9397（1989）。我们观察到，一个积极的场外相互作用增强交错的电荷波动，减少交错的磁秩序。
In the one-dimensional Bose-Hubbard model with on-site and nearest neighbor interactions, a gapped phase characterized by an exotic non-local order parameter emerges, the Haldane insulator. Bose-Hubbard models with cavity-mediated global range interactions display phase diagrams, which are very similar to those with nearest neighbor repulsive interactions, but the Haldane phase remains elusive there. Here we study the one-dimensional Bose-Hubbard model with nearest-neighbor and cavity-mediated global-range interactions and scrutinize the existence of a Haldane Insulator phase. With the help of…
We perform time-resolved exact diagonalization of the Hubbard model with time dependent hoppings on small clusters of up to $12$ sites. Here, the time dependence originates from a classic electromagnetic pulse, which mimics the impact of a photon. We investigate the behavior of the double occupation and spectral function after the pulse for different cluster geometries and on-site potentials. We find impact ionization in all studied geometries except for one-dimensional chains. Adding next-nearest neighbor hopping to the model leads to a significant enhancement of impact ionization, as does di…
We consider a one-dimensional two component extended Fermi-Hubbard model with nearest neighbor interactions and mass imbalance between the two species. We study the stability of trimers, various observables for detecting them, and expansion dynamics. We generalize the definition of the trimer gap to include the formation of different types of clusters originating from nearest neighbor interactions. Expansion dynamics reveal rapidly propagating trimers, with speeds exceeding doublon propagation in strongly interacting regime. We present a simple model for understanding this unique feature of th…
The majority of fulleride superconductors with unusually high transition-temperature to kinetic-energy ratios have a face-centred-cubic (FCC) structure. We demonstrate that, within extended Hubbard models with strong Coulomb repulsion, paired fermions in FCC lattices have qualitatively different properties than pairs in other three-dimensional cubic lattices. Our results show that strongly bound, light, and small pairs can be generated in FCC lattices across a wide range of the parameter space. We estimate that such pairs can Bose condense at high temperatures even if the lattice constant is l…
The charge dynamical response function of the $t-t'-U$ Hubbard model is investigated on the square lattice in the thermodynamical limit. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle-point within the Kotliar and Ruckenstein slave-boson representation. The next-nearest-neighbor hopping only slightly affects the renormalization of the quasiparticle mass. In contrast a negative $t'/t$ notably decreases (increases) their velocity, and hence the zero-sound velocity, at positive (negative) doping. For low (high) density $n \lesssim 0.5$ ($n \gtrsim …
We report a large-scale density-matrix renormalization group study of the lightly doped Hubbard model on 4-leg cylinders at hole doping concentration $δ=12.5\%$. By keeping a large number of states for long system sizes, we are able to reveal a delicate interplay between superconductivity and charge and spin density wave orders tunable via next-nearest neighbor hopping t'. For finite t', the ground state is consistent with that of a Luther-Emery liquid, having `half-filled' charge stripes with power-law superconducting and charge-density-wave correlations of wave-length $λ=1/2δ$, but short-ran…
The variational cluster approximation is used to study the isotropic triangular-lattice Hubbard model at half filling, taking into account the nearest-neighbor ($t_1$) and next-nearest-neighbor ($t_2$) hopping parameters for magnetic frustrations. We determine the ground-state phase diagram of the model. In the strong correlation regime, the 120$^\circ$ Néel and stripe ordered phases appear, and a nonmagnetic insulating phase emerges in between. In the intermediate correlation regime, the nonmagnetic insulating phase expands to a wider parameter region, which goes into a paramagnetic metallic …
The paramagnetic phase of the extended attractive Hubbard model on the cubic lattice is studied within the spin rotation invariant Kotliar-Ruckenstein slave-boson representation at zero temperature. It is obtained that the quasiparticle residue of the Fermi liquid phase vanishes for all densities at an interaction strength slightly smaller than $U_c$ that signals the Brinkman-Rice transition, and that it weakly depends on density. While for vanishing non-local interaction parameters homogeneous static charge instabilities are found in a rather narrow window centered around quarter filling and …
The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground-state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest and next-nearest neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find …
We study the thermodynamics of a zero-dimensional, cubic cluster described with a Hubbard Hamiltonian, focusing our interest on the magnetic properties. The range in which the studied cluster is paramagnetic is considered. The results are obtained by means of exact numerical diagonalization. Such thermodynamic quantities as entropy, specific heat, magnetic susceptibility, spin-spin correlations and double occupancy are discussed. Particular emphasis is put on the behaviour of local maxima of specific heat and susceptibility, which are analysed in terms of Schottky anomalies.
Motivated by the recent discovery of the anomalously nearest-neighbor attraction arising from the electron-phonon coupling, we quantitatively investigate the enhancing effects of this additional attractive channel on the $d$-wave SC based on dynamic cluster quantum Monte Carlo calculations of doped two-dimensional extended Hubbard model with nearest-neighbor attraction $-V$. Focusing on the range of $0<-V/t \le 2$, our simulations indicate that the dynamics of $d$-wave projected pairing interaction is attractive at all frequencies and increases with $|V|$. Moreover, turning on $-V$ attraction …
Quantum Monte Carlo Simulation of Bipolaron Superconductivity in Extended Hubbard--Holstein models on Face-Centered-Cubic and Body-Centered-Cubic Lattices
In the quest for quantum spin liquids in three spatial dimensions (3D), we study the half-filled Hubbard model on the simple cubic lattice with hopping processes up to third neighbors. Employing the variational cluster approach (VCA), we determine the zero-temperature phase diagram: In addition to a paramagnetic metal at small interaction strength $U$ and various antiferromagnetic insulators at large $U$, we find an intermediate-$U$ antiferromagnetic metal. Most interestingly, we also identify a non-magnetic insulating region, extending from intermediate to strong $U$. Using VCA results in the…
In the paper the thermodynamics of a cubic cluster with 8 sites at quarter filling is characterized by means of exact diagonalization technique. Particular emphasis is put on the behaviour of such response functions as specific heat and magnetic susceptibility. The system is modelled with extended Hubbard model which includes electron hopping between both first and second nearest neighbours as well as coulombic interactions, both on-site and between nearest-neighbour sites. The importance of hopping between second nearest neighbours and coulombic interactions between nearest neighbours for the…
We analyze the dynamical nearest-neighbor and next-nearest-neighbor spin correlations in the 4-site and 8-site dynamical cluster approximation to the two-dimensional Hubbard model. Focusing on the robustness of these correlations at long imaginary times, we reveal enhanced ferromagnetic correlations on the lattice diagonal, consistent with the emergence of composite spin-1 moments at a temperature scale that essentially coincides with the pseudo-gap temperature $T^*$. We discuss these results in the context of the spin-freezing theory of unconventional superconductivity.
Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility---ultimately signalling charge instability and phase separation---and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and t…
All van Hove singularities in the density of states (DOS) of face-centered cubic lattice in the nearest and next-nearest neighbour approximation, focusing on higher-order ones, are found and classified. At special values of the ratio $τ$ of nearest and next-nearest neighbour hopping integrals, $t$ and $t'$, giant DOS singularities, caused by van Hove lines or surfaces, are formed. An exact formula for DOS which provides efficient numerical implementation is proposed. The standard tetrahedron method is demonstrated to be inapplicable due to its poor convergence in the vicinity of kinks caused b…
