Hubbard-like Hamiltonian Research Articles

Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation

It is pointed out that the low energy effective theory of a generalized spin system relates to the more generalized system shown by the Hubbard-like model. When the onsite repulsion is assumed to be provided by hard-core repulsion, a generalized fermion with flavour and colour degrees of freedom is used to define the Hubbard-like Hamiltonian in this case. In the strong coupling limit and at half filling this reduces to an antiferromagnet. The <I>D</I>-theory then helps us to associate the continuum limit of the <i>(4+1)D </i>aniferromagnet to <i>4D </i>principal chiral model. It has been observed that in the strong coupling limit the problem of finding the ground state of lattice QCD is identical to that of solving the generalized antiferromagnet with Neel order playing the role of chiral symmetry breaking. In view of this, now formulate the Hubbard-like model Hamiltonian in terms of the gener- alized fermions with flavor and color degrees of freedom also shall consider the<i> D</i>-theoretical framework to show that the antiferromagnetic system which arises in the strong coupling limit and at half filling corresponds to the principal chiral model in the continuum limit with dimensional reduction. Also pointed out that at strong coupling and half filling the system reduces to a Heisenberg antiferromagnet. This result is analogous to the result obtained in standard Hubbard model.

Quantum entanglement of anyon composites

Studying quantum entanglement in systems of indistinguishable particles, in particular anyons, poses subtle challenges. Here, we investigate a model of one-dimensional anyons defined by a generalized algebra. This algebra has the special property that fermions in this model are composites of anyons. A Hubbard-like Hamiltonian is considered that allows hopping between nearest neighbor sites not just for the fundamental anyons, but for the fermionic anyon composites. Some interesting results regarding the quantum entanglement of these particles are obtained.

Effective momentum-momentum coupling in a correlated electronic system

We present a way of partly reincorporate the effects of the localized bonding electrons on the dynamics of their itinerant counterparts in Hubbard-like Hamiltonians. This is done by relaxing the constraint that the former should be entirely frozen in the chemical bonds between the underlying lattice sites through the employment of a Born-Oppenheimer-like ansatz for the wavefunction of the whole electronic system. Accordingly, the latter includes itinerant as well as bonding electron coordinates. Going beyond the adiabatic approximation, we show that the net effect of virtual transitions of bonding electrons between their ground and excited states is to furnish the itinerant electrons with an effective inter-electronic momentum-momentum interaction. Although we have applied these ideas to the specific case of rings, our assumptions can be generalized to higher dimensional systems sharing the required properties of which we have made use herein.

Hidden magnetism in periodically modulated one dimensional dipolar fermions

The experimental realization of time-dependent ultracold lattice systems has paved the way towards the implementation of new Hubbard-like Hamiltonians. We show that in a one-dimensional two-components lattice dipolar Fermi gas the competition between long range repulsion and correlated hopping induced by periodically modulated on-site interaction allows for the formation of hidden magnetic phases, with degenerate protected edge modes. The magnetism, characterized solely by string-like nonlocal order parameters, manifests in the charge and/or in the spin degrees of freedom. Such behavior is enlighten by employing Luttinger liquid theory and numerical methods. The range of parameters for which hidden magnetism is present can be reached by means of the currently available experimental setups and probes.

Mixed-Valence Triferrocenium Complex with Electric Field Controllable Superexchange as a Molecular Implementation of Triple Quantum Dot

In this article, we propose molecular implementation of the quantum logic gate originally realized by the linear triple-quantum dot array accommodating two electrons. To reach this goal we propose to employ the mixed-valence triferrocenium complex exhibiting three isomeric forms with different oxidation degrees FeIII–FeII–FeIII, FeIII–FeIII–FeII, and FeII–FeIII–FeIII, which correspond to three instant localizations of the two holes over three iron ions. The long-range interaction between the terminal metal sites is considered in the framework of the Hubbard-like Hamiltonian which accounts for the electron transfer and inter- and intrasite Coulomb repulsion and takes into account differences in the orbital energies of FeIII and FeII ions. The interaction of the electrons with the applied electric field is also included in the Hamiltonian. It is shown that due to long-range superexchange between the two electronic spins the ground state of the triferrocenium complex is always a spin-singlet, and the first e...

Hubbard-like Hamiltonians for interacting electrons ins,p, anddorbitals

Hubbard-like Hamiltonians are widely used to describe on-site Coulomb interactions in magnetic and strongly-correlated solids, but there is much confusion in the literature about the form these Hamiltonians should take for shells of p and d orbitals. This paper derives the most general s, p and d orbital Hubbard-like Hamiltonians consistent with the relevant symmetries, and presents them in ways convenient for practical calculations. We use the full configuration interaction method to study p and d orbital dimers and compare results obtained using the correct Hamiltonian and the collinear and vector Stoner Hamiltonians. The Stoner Hamiltonians can fail to describe properly the nature of the ground state, the time evolution of excited states, and the electronic heat capacity.

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions.

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.

Effective Hamiltonian for the hybrid double quantum dot qubit

Quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single qubit and two qubits quantum logic ports. We derive the Schrieffer-Wolff effective Hamiltonian that describes in a simple and intuitive way the qubit by combining a Hubbard-like model with a projector operator method. As a result, the Hubbard-like Hamiltonian is transformed in an equivalent expression in terms of the exchange coupling interactions between pairs of electrons. The effective Hamiltonian is exploited to derive the dynamical behaviour of the system and its eigenstates on the Bloch sphere to generate qubits operation for quantum logic ports. A realistic implementation in silicon and the coupling of the qubit with a detector are discussed.

Effective low-energy Hamiltonians for interacting nanostructures

We present a functional renormalization group (fRG) treatment of trigonal graphene nanodiscs and composites thereof, modeled by finite-size Hubbard-like Hamiltonians with honeycomb lattice structure. At half filling, the noninteracting spectrum of these structures contains a certain number of half-filled states at the Fermi level. For the case of trigonal nanodiscs, including interactions between these degenerate states was argued to lead to a large ground state spin with potential spintronics applications. Here we perform a systematic fRG flow where the excited single-particle states are integrated out with a decreasing energy cutoff, yielding a renormalized low-energy Hamiltonian for the zero-energy states that includes effects of the excited levels. The numerical implementation corroborates the results obtained with a simpler Hartree-Fock treatment of the interaction effects within the zero-energy states only. In particular, for trigonal nanodiscs the degeneracy of the one-particle-states with zero-energy turns out to be very robust against influences of the higher levels. As an explanation, we give a general argument that within this fRG scheme the zero-energy degeneracy remains unsplit under quite general conditions and for any size of the trigonal nanodisc. We furthermore discuss the differences in the effective Hamiltonian and their ground states of single nanodiscs and composite bow-tie-shaped systems.

Realistic many-body models for manganese monoxide under pressure

In materials like transition metals oxides where electronic Coulomb correlations impede a description in terms of standard band-theories, the application of genuine many-body techniques is inevitable. Interfacing the realism of density-functional based methods with the virtues of Hubbard-like Hamiltonians, requires the joint ab initio construction of transfer integrals and interaction matrix elements (like the Hubbard U) in a localized basis set. In this work, we employ the scheme of maximally localized Wannier functions and the constrained random phase approximation to create effective low-energy models for Manganese monoxide, and track their evolution under external pressure. We find that in the low pressure antiferromagnetic phase, the compression results in an increase of the bare Coulomb interaction for specific orbitals. As we rationalized in recent model considerations [Phys. Rev. B 79, 235133 (2009)], this seemingly counter-intuitive behavior is a consequence of the delocalization of the respective Wannier functions. The change of screening processes does not alter this tendency, and thus, the screened on-site component of the interaction - the Hubbard U of the effective low-energy system - increases with pressure as well. The orbital anisotropy of the effects originates from the orientation of the orbitals vis-a-vis the deformation of the unit-cell. Within the high pressure paramagnetic phase, on the other hand, we find the significant increase of the Hubbard U is insensitive to the orbital orientation and almost exclusively owing to a substantial weakening of screening channels upon compression.

Electronic spectrum of a helically Hund-coupled [formula omitted]- MnO 2

X-ray diffraction (XRD) and X-ray photoemission (XPS) were used to investigate a high-quality β - MnO 2 thin film epitaxially grown on oriented MgO(001) substrate by plasma-assisted molecular beam epitaxy (PAMBE). Electronic spectrum and energy gap of the β - MnO 2 were computed by local density approximation plus dynamical mean-field theory (LDA+DMFT) in Wannier function basis for a material-specific multiband Hubbard-like Hamiltonian. In the vicinity of Fermi surface, the shape of the calculated electronic spectrum is in good overall agreement with experimental XPS figure.

Density-functional study of the evolution of the electronic structure of oligomers of thiophene: Towards a model Hamiltonian

We present density-functional and time-dependent density-functional studies of the ground, ionic, and excited states of a series of oligomers of thiophene. We show that, for the physical properties, the most relevant highest occupied and lowest unoccupied molecular orbitals develop gradually from monomer molecular orbitals into occupied and unoccupied broad bands in the large length limit. We show that band gap and ionization potentials decrease with size, as found experimentally and from empirical calculations. This gives credence to a simple tight-binding model Hamiltonian approach to these systems. We demonstrate that the length dependence of the experimental excitation spectra for both singlet and triplet excitations can be very well explained with an extended Hubbard-like Hamiltonian, with a monomer on-site Coulomb and exchange interaction and a nearest-neighbor Coulomb interaction. We also study the ground and excited-state electronic structures as functions of the torsion angle between the units in a dimer, and find almost equal stabilities for the transoid and cisoid isomers, with a transition energy barrier for isomerization of only 4.3 kcal/mol. Fluctuations in the torsion angle turn out to be very low in energy, and therefore of great importance in describing even the room-temperature properties. At a torsion angle of 90° the hopping integral is switched off for the highest occupied molecular orbital levels because of symmetry, allowing a first-principles estimate of the on-site interaction minus the next-neighbor Coulomb interaction as it enters in a Hubbard-like model Hamiltonian.

Phase diagram regions deduced for strongly correlated systems via unitary transformation

From known phase diagram regions of different model Hamiltonians describing strongly correlated systems we deduced new domains of the ground state phase diagram of the same model by an unitary transformation. Different types of extended Hubbard Hamiltonians were used for the starting point and the existence of new stable spin-density wave, charge-density wave, ferromagnetic state and a paramagnetic insulator is demonstrated. The used procedure itself is dimension independent.

Charged trans polyacetylene: a density-functional study

In this paper we study the electronic properties of a single doped chain of trans polyacetylene. First, we discuss the different theoretical approaches for studying infinite, periodic, charged chains within parameter-free, electronic-structure calculations. Subsequently, one of these is applied for trans polyacetylene using a density-functional-based method. In particular, the bond-length alternation and the energy gain due to this alternation as a function of added charge are studied. Thereby, it is demonstrated that trans polyacetylene is lacking an electron–hole symmetry. We also explore whether the density-functional calculations predict a too large bond-length alternation when a finite set of points is used in the k-space sampling. Finally, the first-principles results are analysed within a many-body Hubbard-like model Hamiltonian. We find that when extra charge is added to every cell the resulting Hubbard parameters are considerably larger than the ones usually attributed to trans polyacetylene and closer in value to those of the isolated atom. We discuss this result in relation to the importance of screening effects and structural relaxations.

Structural Dependence of Electronic and Magnetic Properties of the Cr13 Cluster**The project supported by National Natural Science Foundation of China

A tight-binding effective potential has been employed, in conjunction with a genetic algorithm, to fully optimize the Cr13 cluster geometry without imposing any symmetry constraints. The minimum energy structure of this cluster is found to be a slightly distorted icosahedron. Based on the optimized structure and three assumed geometries (icosahedron,bcc-like and fcc-like), the structural dependence of electronic and magnetic properties of the Cr13 cluster is discussed by using a d-band Hubbard-like Hamiltonian in the unrestricted Hartree-Fock approximation. Results are given for the average magnetic moment and local magnetic moments. It is found that for all considered geometries the Cr13 cluster exhibits antiferromagnetic behavior. Results are also given for the cohesive energy, average coordination number, and local electronic densities of states. The results indicate that the average coordination number per atom in the cluster geometry is a significant factor to affect the magnetism.Also, the local density of states is a sensitive function of geometry.

Magnetic properties of3dtransition-metal nanostructures: Cr and V clusters embedded in bulk Fe

The magnetic and electronic properties of ${\mathrm{Cr}}_{N}$ and ${\mathrm{V}}_{N}$ clusters embedded in Fe are determined by using a realistic $\mathrm{spd}$-band Hubbard-like model Hamiltonian. The spin-density distribution is calculated self-consistently in the unrestricted Hartree-Fock approximation. The local magnetic moments $\ensuremath{\mu}(i)$ and the densities of electronic states ${\ensuremath{\rho}}_{i}(\ensuremath{\varepsilon})$ are obtained at different atoms $i$ of the cluster and of the surrounding Fe matrix. For all the studied clusters $(N&lt;~51\mathrm{atoms})$ the interface magnetic coupling between cluster and matrix moments is antiparallel. The $\ensuremath{\mu}(i)$ of Cr or V atoms at the interface are enhanced by the presence of Fe atoms in their first-nearest-neighbor shell. In most cases the Fe moments close to the cluster are slightly reduced. In ${\mathrm{Cr}}_{N}$ the interface $\ensuremath{\mu}(i)$ are often much larger than the Cr bulk moments [e.g., $\ensuremath{\mu}(i)=\ensuremath{-}1.30{\ensuremath{\mu}}_{B}$ for ${\mathrm{Cr}}_{4}$ in Fe]. In ${\mathrm{V}}_{N}$ large $\ensuremath{\mu}(i)$ are induced which decrease as $N$ increases or as we move from the interface to the interior of the cluster [e.g., $\ensuremath{\mu}(i)=\ensuremath{-}1.29{\ensuremath{\mu}}_{B}$ for ${\mathrm{V}}_{4}$ in Fe]. A remarkable interplay between the antiferromagnetism of Cr, the paramagnetism of V, and the ferromagnetism of Fe is obtained. The magnetic order within ${\mathrm{Cr}}_{N}$ $({\mathrm{V}}_{N})$ changes from ferromagnetic to antiferromagnetic for $N&gt;~9$ $(N&gt;~6).$ This results in an interesting size dependence of the cluster electronic density of states.

Electronic Structure of InXNa60-X Fullerenes

The electronic properties of the InxNa60—x (x = 1., 60) fullerenes are studied by using a sp Hubbard-like tight-binding Hamiltonian in the unrestricted Hartree-Fock approximation. In particular, we discuss the stability the of the fullerenes In70, In74, In78 and In48Na12 since they are very likely to occur in the hexagonal phases of the ternary compounds Na96In97Z2 and Na172In197Z2 (Z=nickel, palladium, or platinum). Moreover, We determine the electronic structure and stability of In20, In60, In240, In540 and several geometrical arrangements of In48Na12 having all spherical shape. Cylindrical shape like structures In80, In110, In160, and In260 have also been considered. The relation between the calculated electronic properties and the fullerene geometry is analyzed. The perspectives of extensions of this study are also briefly discussed.

Spectral and magnetic properties of one-dimensional superlattices

We investigated the electron correlation effects in one-dimensional superlattices composed of free (uncorrelated) and repulsive (correlated) sites, using Lanczos diagonalization of chains of up to ten sites described by a Hubbard-like Hamiltonian. The electronic and magnetic properties are shown to depend primarily on the splitting between single-site energies for the correlated and uncorrelated orbitals, respectively, and on the average electron density in the system. The local moments and spin-spin correlations are closely related to the changes in the conductivity, and the magnetic properties are enhanced when the insulating regime is approached. Irrespective of the type of superlattice considered, the local moments form on the correlated orbitals, and may only be induced on single uncorrelated orbitals which separate correlated clusters. The transition from metallic to insulating behaviour can be qualitatively understood in terms of a strongly correlated model, with two Hubbard subbands due to strong Coulomb interactions accompanied by a metallic band of uncorrelated states.

Noncollinear magnetism in disordered alloys and intermetallic compounds

Ab-initio calculations of the ground state of non-collinear magnets based on local-spin-density and Hubbard-like Hamiltonians and using a tight-binding linear-muffin-tin orbital (TB-LMTO) basis are described. Detailed results are given for substitutional alloys showing spin-glass behaviour, for disordered intermetallic compounds and for amorphous metals and alloys.

Correlation Effects of the Ferromagnetic State in Single Band Model

Using the local approach, we have discussed correlation effects in the ferromagnetic state with a Hubbard-like tight-binding Hamiltonian. The results show that the correlation effect in the ferromagnetic state is stronger than in the paramagnetic one, and the correlation of electrons mainly depend on the Coulomb interaction, the contribution of the exchange interaction to the correlation effects is very small.