Extended Hubbard Model Research Articles

Dual boson diagrammatic Monte Carlo approach applied to the extended Hubbard model

In this work we introduce the Dual Boson Diagrammatic Monte Carlo technique for strongly interacting electronic systems. This method combines the strength of dynamical mean-filed theory for non-perturbative description of local correlations with the systematic account of non-local corrections in the Dual Boson theory by the diagrammatic Monte Carlo approach. It allows us to get a numerically exact solution of the dual boson theory at the two-particle local vertex level for the extended Hubbard model. We show that it can be efficiently applied to description of single particle observables in a wide range of interaction strengths. We compare our exact results for the self-energy with the ladder Dual Boson approach and determine a physical regime, where description of collective electronic effects requires more accurate consideration beyond the ladder approximation. Additionally, we find that the order-by-order analysis of the perturbative diagrammatic series for the single-particle Green's function allows to estimate the transition point to the charge density wave phase.

One-Dimensional Alternating Extended Hubbard Model at Quarter-Filling and Its Applications to Structural Instabilities of Organic Conductors

The one-dimensional extended Hubbard model with lattice dimerization and alternated site potentials is analyzed using the renormalization group method. The coupling of electrons to structural degrees of freedom such as the anion lattice and acoustic phonons is investigated to obtain the possible instabilities against the formation of lattice superstructures. Applications of the theory to anionic and spin-Peierls instabilities in the Fabre and Bechgaard salts series of organic conductors and ordered alloys are presented and discussed.

Parameter-free hybridlike functional based on an extended Hubbard model: DFT+U+V

In this article, we propose an energy functional at the level of DFT+U+V that allows us to compute self-consistently the values of the on-site interaction, Hubbard U and Hund J, as well as the intersite interaction V. This functional extends the previously proposed ACBN0 functional [Phys. Rev. X 5, 011006 (2015)] including both on-site and intersite interactions. We show that this ab initio self-consistent functional yields improved electronic properties for a wide range of materials, ranging from $sp$ materials to strongly-correlated materials. This functional can also be seen as an alternative general and systematic way to construct parameter-free hybrid functionals, based on the extended Hubbard model and a selected set of Coulomb integrals, and might be used to develop novel approximations. By extending the DFT+U method to materials where strong local and nonlocal interactions are relevant, this work opens the door to the ab initio study the electronic, ionic, and optical properties of a larger class of strongly correlated materials in and out of equilibrium.

η -pairing states as true scars in an extended Hubbard model

The eta-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called "eta-pairing SU(2)" symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [Physica C 158, 326 (1989)], where the eta-pairing states survive without the eta-pairing symmetry and become true scar states. We also discuss similarities between the eta-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in 1D. We also generalize these terms to arbitrary bipartite lattices. Our study of the spin-1 XY model also leads us to several new scarred models, including a spin-1/2 $J_1-J_2$ model with Dzyaloshinkskii-Moriya interaction, in realistic quantum magnet settings in 1D and 2D.

Competition between Interactions and Randomness in Photoinduced Synchronization of Charge Oscillations on a Dimer Lattice

The synchronization of charge oscillations after photoexcitation that has been realized through the emergence of an electronic breathing mode on dimer lattices is studied here from the viewpoint of the competition between interactions and randomness. We employ an extended Hubbard model at three-quarter filling on a simple dimer lattice and add random numbers to all transfer integrals between nearest-neighbor sites. Photoinduced dynamics are calculated using the time-dependent Schr\"odinger equation by the exact diagonalization method. Although the randomness tends to unsynchronize charge oscillations on different bonds during and after photoexcitation, sufficiently strong on-site repulsion $U$ overcomes this effect and synchronizes these charge oscillations some time after strong photoexcitation. The degree of synchronization is evaluated using an order parameter that is derived from the time profiles of the current densities on all bonds. As to the nearest-neighbor interaction $V$, if $V$ is weakly attractive, it increases the order parameter by facilitating the charge oscillations. The relevance of these findings to previously reported experimental and theoretical results for the organic conductor $\kappa$-(bis[ethylenedithio]tetrathiafulvalene)$_2$Cu[N(CN)$_2$]Br is discussed.

Light-Induced Renormalization of the Dirac Quasiparticles in the Nodal-Line Semimetal ZrSiSe.

In nodal-line semimetals, linearly dispersing states form Dirac loops in the reciprocal space with a high degree of electron-hole symmetry and a reduced density of states near the Fermi level. The result is reduced electronic screening and enhanced correlations between Dirac quasiparticles. Here we investigate the electronic structure of ZrSiSe, by combining time- and angle-resolved photoelectron spectroscopy with abinitio density functional theory (DFT) complemented by an extended Hubbard model (DFT+U+V) and by time-dependent DFT+U+V. We show that electronic correlations are reduced on an ultrashort timescale by optical excitation of high-energy electrons-hole pairs, which transiently screen the Coulomb interaction. Our findings demonstrate an all-optical method for engineering the band structure of a quantum material.

Spin resonances in iron selenide high- Tc superconductors by proximity to a hidden spin density wave

Recent inelastic neutron scattering studies by Pan et al., Nature Communications 8, 123 (2017), find evidence for spin excitations at energies above the quasi-particle gap in an iron-selenide high-Tc superconductor. The momenta of the spin excitations form a diamond around the checkerboard wavevector, Q_AF, that is associated with the square lattice of iron atoms that makes up the system. It has been suggested that such a "hollowed-out" spin-excitation spectrum is due to hidden Neel order. We study such a hidden spin-density wave (hSDW) state that results from nested Fermi surfaces at the center and at the corner of the unfolded Brillouin zone. It emerges within mean field theory from an extended Hubbard model over a square lattice of iron atoms that contain the minimal d_xz and d_yz orbitals. Opposing Neel order exists over the isotropic d+ = d_xz + i d_yz and d- = d_xz - i d_yz orbitals. The dynamical spin susceptibility of the hSDW is computed within the random phase approximation, at perfect nesting. Unobservable Goldstone modes that disperse acoustically are found at Q_AF. A threshold is found in the spectrum of observable spin excitations that forms a "floating ring" at Q_AF also. The ring threshold moves down in energy toward zero with increasing Hund's Rule coupling, while it moves up in energy with increasing magnetic frustration. Comparison with the normal-state features of the spin-excitation spectrum shown by electron-doped iron selenide is made. Also, recent predictions of a Lifshitz transition from the nested Fermi surfaces to Fermi surface pockets at the corner of the folded Brillouin zone will be discussed.

Robust spin and charge excitations throughout the high- Tc cuprate phase diagram from incipient Mottness

The generic phase diagram of lightly hole-doped high-$T_c$-cuprates hosts antiferromagnetic insulating phase with well-defined spin-wave excitations. Contrary to the weak-coupling prediction, these modes persist up to the overdoped metallic regime as intense and dispersive paramagnons. Here we report on our study of the low-energy magnetic and charge excitations within the extended Hubbard model at strong-coupling, using a modified $1/N$ expansion method with a variational state serving as the saddle point solution. Despite clear separation of magnetic and Hubbard-$U$ energy scales, we find that incipient Mottness affects qualitatively dispersions and widths of magnetic modes throughout entire phase diagram. The obtained magnetic and charge dynamical structure factors agree semi-quantitatively with recent resonant $X$-ray and neutron scattering data for $\mathrm{La_{2-\mathit{x}}Sr_\mathit{x}CuO_4}$ and $\mathrm{(Bi,Pb)_2(Sr,La)_2CuO_{6+\delta}}$ at all available doping levels. The weak-coupling random-phase-approximation fails already for underdoped samples, pointing to the non-trivial intertwining of distinct energy scales in cuprate superconductors. The existence of a discrete charge mode which splits off the electron-hole continuum is also predicted.

Minimal model of charge and pairing density waves in x-ray scattering experiments

Competing density waves play an important role in the mystery of high-temperature superconductors. In spite of the large amount of experimental evidence, the fundamental question of whether these modulations represent charge or pairing density waves (CDWs or PDWs) is still debated. Here we present a method to answer this question using momentum and energy-resolved resonant X-ray scattering maps. Starting from a minimal model of density waves in superconductors, we identify distinctive signatures of incipient CDWs and PDWs. The generality of our approach is confirmed by a self-consistent solution of an extended Hubbard model with attractive interaction. By considering the available experimental data, we claim that the spatial modulations in cuprates have a predominant PDW character. Our work paves the way for using X-ray to identify competing and intertwined orders in superconducting materials.

Topological phases arising from attractive interaction and pair hopping in the extended Hubbard model

The extended Hubbard model with an attractive density–density interaction, positive pair hopping, or both, is shown to host topological phases, with a doubly degenerate entanglement spectrum and interacting edge spins. This constitutes a novel instance of topological order which emerges from interactions. When the interaction terms combine in a charge-SU(2) symmetric fashion, a novel partially polarized pseudospin phase appears, in which the topological features of the spin degrees of freedom coexist with long-range η-wave superconductivity. Thus, our system provides an example of an interplay between spontaneous symmetry breaking and symmetry-protected topological order that leads to novel and unexpected properties.

Superconductivity in Electronic Systems with Strong Correlations

We report a consistent microscopic theory of superconductivity for strongly correlated electronic systems. The electronic spectrum and superconductivity are studied using the Bogoliubov–Tyablikov Green functions for the projected (Hubbard) electronic operators. The extended Hubbard model is considered where the intersite Coulomb repulsion and the electron-phonon interaction are taken into account. The $$d$$ ‑wave pairing with high- $${{T}_{c}}$$ is found induced by the strong kinematical interaction of electrons with spin fluctuations that proves the spin-fluctuation mechanism of high-temperature superconductivity.

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.

Effect of Coulomb interactions on the Seebeck coefficient of the organic Dirac electron system α−(BEDT-TTF)2I3

Motivated by the results of recent thermoelectric effect studies, we show the effects of Coulomb interactions on the Seebeck coefficient based on an extended Hubbard model that describes the electronic states of a slightly doped organic Dirac electron system, $\alpha$-(BEDT-TTF)$_2$I$_3$. Our results indicate that the Hartree terms of the Coulomb interactions enhance the electron-hole asymmetry of the energy band structure and change the energy dependence of the relaxation time from impurity scattering, which reflects the shape of the density of states. Thus, the Seebeck coefficient exhibits a non-monotonic $T$ dependence which qualitatively agrees with the experimental results. Furthermore, we also show that the signs of the Seebeck coefficient and the Hall coefficient calculated by linear response theory do not necessarily correspond to the sign of the chemical potential using a modified Weyl model with electron-hole asymmetry. These results point out that changing the electron-hole asymmetry by strong Coulomb interaction has the potential to controllable the sign and value of the Seebeck coefficient in the Dirac electron systems.

Mott phase in a van der Waals transition-metal halide at single-layer limit

Two-dimensional materials offer opportunities for unravelling unprecedented ordered states at single layer limit. Among such ordered states, Mott phase is rarely explored. Here, we report the Mott phase in van der Waals chromium (II) iodide (CrI2) films. High quality CrI2 films with atomically flat surface and macro size are grown on graphitized 6H-SiC(0001) substrate by molecular beam epitaxy. By in situ low temperature scanning tunneling microscopy and spectroscopy (STM/STS), we reveal that the film has a band gap as large as ~3.2 eV, which is nearly thickness independent. Density functional plus dynamic mean field theory calculations suggest that CrI2 films may be a strong Mott insulator with a ferromagnetically ordered ground state. The Mott phase is corroborated by the spectral band splitting, that is consistent with the extended Hubbard model, and gap reduction at charge dopants. Our study provides a platform for studying correlated electron states at single layer limit.

Nonequilibrium scenarios in cluster-forming quantum lattice models

We investigate the out-of-equilibrium physics of monodisperse bosonic ensembles on a square lattice. The effective Hamiltonian description of these systems is given in terms of an extended Hubbard model with cluster-forming interactions relevant to experimental realizations with cold Rydberg-dressed atoms. The ground state of the model, recently investigated in Phys. Rev. Lett. 123, 045301 (2019), features, aside from a superfluid and a stripe crystalline phase occurring at small and large interaction strength $V$, respectively, a rare first-order transition between an isotropic and an anisotropic stripe supersolid at intermediate $V$. By means of quantum Monte Carlo calculations we show that the equilibrium crystal may be turned into a glass by simulated temperature quenches and that out-of-equilibrium isotropic (super)solid states may emerge also when their equilibrium counterparts are anisotropic. These out-of-equilibrium states are of experimental interest, their excess energy with respect to the ground state being within the energy window typically accessed in cold atom experiments. We find, after quenching, no evidence of coexistence between superfluid and glassy behavior. Such an absence of superglassiness is qualitatively explained.

Collapse of the vacuum in hexagonal graphene quantum dots: A comparative study between tight-binding and mean-field Hubbard models

In this paper, we perform a systematic study on the electronic, magnetic, and transport properties of the hexagonal graphene quantum dots (GQDs) with armchair edges in the presence of a charged impurity using two different configurations: (1) a central Coulomb potential and (2) a positively charged carbon vacancy. The tight binding (TB) and the half-filled extended Hubbard models are numerically solved and compared with each other in order to reveal the effect of electron interactions and system sizes. Numerical results point out that off-site Coulomb repulsion leads to an increase in the critical coupling constant to $\beta_{\text{c}}$ = 0.6 for a central Coulomb potential. This critical value of the $\beta$ is found to be independent of GQD size, reflecting its universality even in the presence of electron-electron interactions. In addition, a sudden downshift in the transmission peaks shows a clear signature of the transition from subcritical $\beta$ $<$ $\beta_{\text{c}}$ to supercritical $\beta$ $>$ $\beta_{\text{c}}$ regime. On the other hand, for a positively charged vacancy, the collapse of the lowest bound state occurs at $\beta_{\text{c}}$ = 0.7 for the interacting case. Interestingly, the local magnetic moment, induced by a bare carbon vacancy, is totally quenched when the vacancy is subcritically charged, whereas the valley splittings in electron and hole channels continue to exist in both regimes.

Characterization of photoexcited states in the half-filled one-dimensional extended Hubbard model assisted by machine learning

Photoinduced nonequilibrium states can provide new insight into dynamical properties of strongly correlated electron systems. One of the typical and extensively studied systems is the half-filled one-dimensional extended Hubbard model (1DEHM). Here, we propose that the supervised machine learning (ML) can provide useful information for characterizing photoexcited states in 1DEHM. Using entanglement spectra as a training dataset, we construct neural network. Judging from the trained network, we find that bond-spin-density wave (BSDW) order can be enhanced in photoexcited states if the frequency of a driving pulse nearly resonates with gap. We separately calculate the time evolution of local and non-local order parameters and confirm that the correlation functions of BSDW are actually enhanced by photoexcitation as predicted by ML. The successful prediction of BSDW demonstrates the advantage of ML to assist characterizing photoexcited quantum states.

Detecting superconductivity out of equilibrium

Recent pump-probe experiments on underdoped cuprates and similar systems suggest the existence of a transient superconducting state above $\mathrm{T}_c$. This poses the question how to reliably identify the emergence of long-range order, in particular superconductivity, out-of-equilibrium. We investigate this point by studying a quantum quench in an extended Hubbard model and by computing various observables, which are used to identify (quasi-)long-range order in equilibrium. Our findings imply that, in contrast to current experimental studies, it does not suffice to study the time evolution of the optical conductivity to identify superconductivity. In turn, we suggest to utilize time-resolved ARPES experiments to probe for the formation of a condensate in the two-particle channel.

Antiferromagnetism and chiral d -wave superconductivity from an effective t−J−D model for twisted bilayer graphene

Starting from the strong-coupling limit of an extended Hubbard model, we develop a spin-fermion theory to study the insulating phase and pairing symmetry of the superconducting phase in twisted bilayer graphene. Assuming that the insulating phase is an anti-ferromagnetic insulator, we show that fluctuations of the anti-ferromagnetic order in the conducting phase can mediate superconducting pairing. Using a self-consistent mean-field analysis, we find that the pairing wave function has a chiral d-wave symmetry. Consistent with this observation, we show explicitly the existence of chiral Majorana edge modes by diagonalizing our proposed Hamiltonian on a finite-sized system. These results establish twisted bilayer graphene as a promising platform to realize topological superconductivity.

Generic Optical Excitations of Correlated Systems: π-tons.

The interaction of light with solids gives rise to new bosonic quasiparticles, with the exciton being-undoubtedly-the most famous of these polaritons. While excitons are the generic polaritons of semiconductors, we show that for strongly correlated systems another polariton is prevalent-originating from the dominant antiferromagnetic or charge density wave fluctuations in these systems. As these are usually associated with a wave vector (π,π,…) or close to it, we propose to call the derived polaritons π-tons. These π-tons yield the leading vertex correction to the optical conductivity in all correlated models studied: the Hubbard, the extended Hubbard model, the Falicov-Kimball, and the Pariser-Parr-Pople model, both in the insulating and in the metallic phase.