Two-dimensional Extended Hubbard Model Research Articles

Two-dimensional extended Hubbard model: doping, next-nearest neighbor hopping and phase diagrams

Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping , less mobile carriers produce a stronger fall in v c . For half-filling and , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.

Two-dimensional extended Hubbard model at half-filling

We consider the extended Hubbard model on a two-dimensional square lattice at half-filling. The model is investigated using the strong coupling diagram technique. We sum infinite series of ladder diagrams allowing for full-scale charge and spin fluctuations and the actual short-range antiferromagnetic order for nonzero temperatures. In agreement with earlier results, we find the first-order phase transition in the charge subsystem occurring at v = v c ≳ U/4 with v and U the intersite and on-site Coulomb repulsion constants. The transition reveals itself in an abrupt sign change of a sharp maximum in the zero-frequency charge susceptibility at the corner of the Brillouin. States arising at the transition have alternating deviations of electron occupations from the mean value on neighboring sites. Due to fluctuations, these alternating occupation deviations have short-range order. For the considered parameters, such behavior is found for U ≲ 5t with t the hopping constant. For the insulating case U ≳ 6t, in which the transition is not observed, we find a continuous growth of the Mott gap with v. The evolution of the electron density of states with increasing v is also considered.

Enhancing d -wave superconductivity with nearest-neighbor attraction in the extended Hubbard model

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 enhances the $(\pi,\pi)$ spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at $V/t=-1$ relevant to ``holon folding branch'', the charge fluctuations are insufficient to compete with $d$-wave pairing interaction strengthened by enhanced spin fluctuations. Our work suggest the underlying rich interplay between the spin and charge fluctuations in giving rise to the superconducting properties.

First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling.

The combination of spin-orbit coupling with interactions results in many exotic phases of matter. In this Letter, we investigate the superconducting pairing instability of the two-dimensional extended Hubbard model with both Rashba and Dresselhaus spin-orbit coupling within the mean-field level at both zero and finite temperature. We find that both first- and second-order time-reversal symmetry breaking topological gapped phases can be achieved under appropriate parameters and temperature regimes due to the presence of a favored even-parity s+id-wave pairing even in the absence of an external magnetic field or intrinsic magnetism. This results in two branches of chiral Majorana edge states on each edge or a single zero-energy Majorana corner state at each corner of the sample. Interestingly, we also find that not only does tuning the doping level lead to a direct topological phase transition between these two distinct topological gapped phases, but also using the temperature as a highly controllable and reversible tuning knob leads to different direct temperature-driven topological phase transitions between gapped and gapless topological superconducting phases. Our findings suggest new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superconductors in a simple but realistic microscopic model.

D -wave superconductivity in the presence of nearest-neighbor Coulomb repulsion

Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of $d$-wave pairing when a near neighbor Coulomb repulsion $V$ is present in addition to the on-site Coulomb repulsion $U$. We find that $d$-wave pairing and the superconducting transition temperature $T_c$ are only weakly suppressed as long as $V$ does not exceed $U/2$. This stability is traced to the strongly retarded nature of pairing that allows the $d$-wave pairs to minimize the repulsive effect of $V$. When $V$ approaches $U/2$, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of $d$-wave pairing and $T_c$ than for smaller $V$.

Optical Conductivity in a Two-Dimensional Extended Hubbard Model for an Organic Dirac Electron System α-(BEDT-TTF)2I3

The optical conductivity in the charge order phase is calculated in the two-dimensional extended Hubbard model describing an organic Dirac electron system α -(BEDT-TTF) 2 I 3 using the mean field theory and the Nakano-Kubo formula. Because the interband excitation is characteristic in a two-dimensional Dirac electron system, a peak structure is found above the charge order gap. It is shown that the peak structure originates from the Van Hove singularities of the conduction and valence bands, where those singularities are located at a saddle point between two Dirac cones in momentum space. The frequency of the peak structure exhibits drastic change in the vicinity of the charge order transition.

Photoinduced absorptions inside the Mott gap in the two-dimensional extended Hubbard model

We theoretically investigate pump-probe optical responses in the two-dimensional extended Hubbard model describing cuprates by using a time-dependent Lanczos method. At half filling, pumping generates photoinduced absorptions inside the Mott gap. A part of low-energy absorptions is attributed to the independent propagation of photoinduced holons and doublons. The spectral weight just below the Mott gap increases with decreasing the on-site Coulomb interaction $U$. We find that the next-nearest-neighbor Coulomb interaction $V_1$ enhances this $U$ dependence, indicating the presence of biexcitonic contributions formed by two holon-doublon pairs. Photo-pumping in hole-doped systems also induces spectral weights below remnant Mott-gap excitations, being consistent with recent experiments. The induced weights are less sensitive to $V_1$ and may be related to the formation of a biexcitonic state in the presence of hole carriers.

Charge and magnetic properties of 2D extended Hubbard model

ABSTRACTThe ground state of the two-dimensional Extended Hubbard Model is studied within an exact analytical diagonalization. The Charge and magnetic properties are determined by analyzing the behaviour of charge gap and spin gap as a function of on-site coulomb interaction energy U and spin-spin interaction term J. The obtained results showed that the introduction of long-range off-site interactions induces a vanishing of charge gap and a J independency of spin gap.

Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model

The dual boson approach [Ann. Phys. 327, 1320 (2012)] provides a means to construct a diagrammatic expansion around the extended dynamical mean-field theory (EDMFT). In this paper, we present the numerical implementation of the approach and apply it to the extended Hubbard model with nearest-neighbor interaction $V$. We calculate the EDMFT phase diagram and study the effect of diagrams beyond EDMFT on the transition to the charge-ordered phase. Including diagrammatic corrections to the EDMFT polarization shifts the EDMFT phase boundary to lower values of $V$. The approach interpolates between the random phase approximation in the weak coupling limit and EDMFT for strong coupling. Neglecting vertex corrections leads to results reminiscent of the EDMFT+$GW$ approximation. We however find significant deviations from the dual boson results already for small values of the interaction, emphasizing the crucial importance of fermion-boson vertex corrections.

Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion.

We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from self-consistent extended dynamical mean-field theory and include nonlocal dynamical vertex corrections through a ladder approximation to the polarization operator. This is necessary to fulfill charge conservation and to describe plasmons in the correlated state. The calculated plasmon spectra are qualitatively different from those in the random-phase approximation: they exhibit a spectral density transfer and a renormalized dispersion with enhanced deviation from the canonical √q behavior. Both features are reminiscent of interaction induced changes found in single-electron spectra of strongly correlated systems.

Local magnetic properties of $$L\times L$$ L × L square lattice with an Extended Hubbard Model

Within an analytical diagonalization, it is possible to exactly solve a large class of models useful for the study of strongly correlated electrons systems. Here, we perform an exact diagonalization of the two-dimensional Extended Hubbard Model with first nearest neighbor repulsive $$V$$ and spin-spin interaction $$J$$ at one-eight filling. The analysis of the ground state energy and spin gap behaviors as a function of $$V$$ and $$J$$ terms allows us to study some local magnetic properties of $$2D$$ ferromagnetic correlated electrons system distributed in finite square lattice. The obtained results show the existence of competition between Spin Density Wave and Charge Density Wave with the possibility to have a phase transition between these two waves at a critical value $$V_{c}$$

Unconventional superconducting phases for the two-dimensional extended Hubbard model on a square lattice

We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur at half-filling when 4V > U gives way to a d_{xy} -wave superconducting instability away from half-filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive and a range of on-site repulsive interaction. In addition, when nesting is further suppressed and in presence of a nearest-neighbor attraction, a triplet time-reversal breaking (p_x + ip_y)-wave pairing instability emerges, competing with the d_{x2+y2} pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (p_x +ip_y)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while d_{xy}-pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.

Superconducting Pairing Symmetry on the Extended Hubbard Model in the Presence of the Rashba-Type Spin–Orbit Coupling

In order to study the pairing symmetry in non-centrosymmetric superconductors, we solve the linearized Eliashberg's equation on the two-dimensional extended Hubbard model in the presence of the Rashba-type spin-orbit coupling (RSOC) within the random phase approximation. In the presence of the RSOC, three types of pairing symmetries appear in the phase diagram with respect to the on-site Coulomb repulsion U and off-site one V. Each of pairing symmetries is admixture of spin-singlet and -triplet ones. On the basis of analytical study, it is found that the admixture of spin-singlet and -triplet components depends on not only the predominant pairing symmetry but also dispersion relation and pairing interaction.

Incommensurate nematic fluctuations in the two-dimensional Hubbard model

We analyze effective d-wave interactions in the two-dimensional extended Hubbard model at weak coupling and small to moderate doping. The interactions are computed from a renormalization group flow. Attractive d-wave interactions are generated via antiferromagnetic spin fluctuations in the pairing and charge channels. Above Van Hove filling, the d-wave charge interaction is maximal at incommensurate diagonal wave vectors, corresponding to nematic fluctuations with a diagonal modulation. Below Van Hove filling a modulation along the crystal axes can be favored. The nematic fluctuations are enhanced by the nearest-neighbor interaction in the extended Hubbard model, but they always remain smaller than the dominant antiferromagnetic, pairing, or charge density wave fluctuations.

Fermi Surface Deformation Near Charge-Ordering Transition

We study the deformation of a Fermi surface (FS) near charge-ordering (CO) transition. By applying a fluctuation-exchange approximation to the two-dimensional extended Hubbard model, we show that the FS is largely modified by strong charge fluctuations when the wave number of the CO pattern does not match the nesting vector of the FS in a noninteracting system. We also discuss the enhanced anisotropy in quasiparticle properties in the resultant metallic state.

Pomeranchuk instability on a two-dimensional frustrated lattice

We investigate the Pomeranchuk instability (PI) in the two-dimensional extended Hubbard model with frustration using the variational cluster approach. The system shows a tendency toward the PI which breaks the tetragonal symmetry of the Fermi surface. However, a pure superconducting state with isotropic underlying lattice is more favored for weak nearest-neighbor repulsion $V$. As $V$ is increased beyond the critical value, superconductivity is suppressed and the system undergoes a first-order transition to the PI. We find that the local density of states (LDOS) shows interesting behavior in the presence of Fermi-surface symmetry breaking. The low-energy feature of LDOS is sharp and the spectral weight remarkably transfers from low-energy peaks to the local minimum near the Fermi level. Meanwhile, the high-energy feature remains almost unchanged. Based on these findings, we can establish a potential relationship between the PI and metamagnetic transition in the bilayer ruthenate ${\text{Sr}}_{3}{\text{Ru}}_{2}{\text{O}}_{7}$.

Quantum Critical Behavior of Electrons at the Edge of Charge Order

We consider quantum critical points in which quantum fluctuations associated with charge rather than magnetic order induce unconventional metallic properties. Based on finite-T calculations on a two-dimensional extended Hubbard model, we show how the coherence scale T(*) characteristic of Fermi liquid behavior of the homogeneous metal vanishes at the onset of charge order. A strong effective mass enhancement reminiscent of heavy fermion behavior indicates the possible destruction of quasiparticles at the quantum critical points. Experimental probes on quarter-filled layered organic materials are proposed for unveiling the behavior of electrons across the quantum critical region.

Enhanced Spin Susceptibility toward the Charge-Ordering Transition in a Two-Dimensional Extended Hubbard Model

We investigate the charge and spin susceptibilities in the vicinity of a charge-ordering transition point on the basis of a two-dimensional extended Hubbard model with nearest-neighbor Coulomb interaction on a square lattice. In order to evaluate the leading contribution of vertex corrections, we construct a new iterative method generating a series of non-skeleton diagrammatic conserving approximations, and utilize the first approximation for the calculation of response functions. This approximation can determine a charge-ordering transition point and static susceptibilities on an equal footing in a sense that the compressibility and spin-susceptibility sum rules are satisfied. As a prominent effect of vertex corrections, we find that the uniform spin susceptibility is enhanced owing to charge fluctuations that develop toward the charge-ordering transition. We also discuss the experimental relevance of our theory for organic conductors, together with its connection to Landau's Fermi-liquid theory.

An exact solution to the extended Hubbard model in 2D for finite size system

An exact analytical diagonalization is used to solve the two-dimensional extended Hubbard model (EHM) for a system with finite size. We have considered an EHM including on-site and off-site interactions with interaction energies U and V, respectively, for a square lattice containing 4×4 sites at one-eighth filling with periodic boundary conditions, recently treated by Kovacs and Gulacsi (2006 Phil. Mag. 86 2073). Taking into account the symmetric properties of this square lattice and using a translation linear operator, we have constructed a r-space basis only with 85 state-vectors which describe all possible distributions for four electrons in the 4×4 square lattice. The diagonalization of the 85×85 matrix energy allows us to study the local properties of the above system as a function of the on-site and off-site interactions energies, where we have shown that the off-site interaction encourages the existence of the double occupancies at the first excited state and induces a supplementary conductivity of the system.

Superconductivity and hybridization in a two-dimensional extended Hubbard model: Strong coupling regime

In this work we study the effect of hybridization on the superconductivity within an attractive two-band Hubbard model. We describe the interband effects through an one body mixing term, differently from standard approaches. We consider a s-wave superconducting gap and a Hubbard-I approximation to describe the strongly correlated superconducting regime. We use Greens’ function method to obtain the order parameter Δ 0 and the superconducting critical temperature T c for various values of the hybridization strength V and the attractive potential U. The results show that for fixed values of U and V the gap raises for low temperatures and diminishes abruptly as the temperature increases. Also, T c diminishes as V increases, and there exist a critical value V c for which superconductivity is suppressed.