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An exact Jordan-Wigner type of transformation is presented in 1D connecting spin-1/2 operators to spinful canonical Fermi operators. The transformation contains two free parameters allowing a broad interconnection possibility in between spin models and fermionic models containing spinful Fermi operators., Comment: 9 pages

Based on a positive semidefinite operator technique, exact ground states are deduced for the non-integrable conducting polymers possessing pentagon type of unit cell. The study is done in the presence of many-body spin-orbit interaction (SOI), local and nearest neighbor Coulomb repulsion (NNCR) and presence of external $E$ electric and $B$ magnetic fields, such that the effects of $B$ on both orbital and spin degrees of freedom is considered. The SOI, NNCR, and presented external field configurations presence in exact conducting polymer ground states is a novelty, so the development of the technique for the treatment possibility of such strongly correlated cases is presented in details. The deduced ground states show a broad spectrum of physical characteristics ranging from charge density waves, metal-insulator transitions, to interesting external field driven effects as e.g. modification possibility of a static charge distribution by a static external magnetic field., Comment: 47 pages, 2 figures

Flat bands are of extreme interest in a broad spectrum of fields since given by their high degeneracy, a small perturbation introduced in the system is able to push the ground state in the direction of an ordered phase of interest. Hence the flat band engineering in real materials attracts huge attention. However, manufacturing a flat band represents a difficult task because its appearance in a real system is connected to rigid mathematical conditions relating a part of Hamiltonian parameters. Consequently, whenever a flat band is desired to be manufactured, these Hamiltonian parameters must be tuned exactly to the values fixed by these rigid mathematical conditions. Here we demonstrate that taking the many-body spin-orbit interaction (SOI) into account -- which can be continuously tuned e.g. by external electric fields --, these rigid mathematical conditions can be substantially relaxed. On this line we show that a $\sim 20-30 \%$ variation in the Hamiltonian parameters rigidly fixed by the flat band conditions can also lead to flat bands in the same or in a bit displaced position on the energy axis. This percentage can even increase to $\sim 80 \%$ in the presence of an external magnetic field. The study is made in the case of conducting polymers. These systems are relevant not only because they have broad application possibilities, but also because they can be used to present the mathematical background of the flat band conditions in full generality, in a concise, clear and understandable manner applicable everywhere in itinerant systems.

The ferromagnetism of Au nanograins is analysed based on a two-dimensional itinerant lattice model with on-site Coulomb repulsion, many-body spin-orbit interactions, and holding two hybridized bands, one correlated and one uncorrelated. Using periodic boundary conditions in both directions, an exact ferromagnetic ground state is deduced for this non-integrable system by applying special techniques based on positive semidefinite operators.

A 2D square, two-bands, strongly correlated and non-integrable system is analysed exactly in the presence of many-body spin-orbit interactions via the method of Positive Semidefinite Operators. The deduced exact ground states in the high concentration limit are strongly entangled, and given by the spin-orbit coupling are ferromagnetic and present an enhanced carrier mobility, which substantially differs for different spin projections. The described state emerges in a restricted parameter space region, which however is clearly accessible experimentally. The exact solutions are provided via the solution of a matching system of equations containing 74 coupled, non-linear and complex algebraic equations. In our knowledge, other exact results for 2D interacting systems with spin-orbit interactions are not present in the literature.

We analyze, in exact terms, multiband 2D itinerant correlated fermionic systems with many-body spin-orbit interactions, and in-plane external magnetic fields. Even if such systems with broad applicability in leading technologies are non-integrable, we set up an exact solution procedure for them, which is described in detail. Casting the Hamiltonian in positive semidefinite form, the technique leads to the ground state and also characterizes the low lying excitation spectrum.

We consider a pentagon chain described by a Hubbard type of model considered under periodic boundary conditions. The system i) is placed in an external magnetic field perpendicular to the plane of the cells, and ii) is in a site selective manner under the action of an external electric potential. In these conditions we show in a non-approximated manner that the physical properties of the system can be qualitatively changed. The changes cause first strong modifications of the band structure of the system created by the one-particle part of the Hamiltonian, and second, considerably redraw the emergence domains of ordered phases. We exemplify this by deducing ferromagnetic ground states in the presence of external fields in two different domains of the parameter space., Comment: 23 pages, 6 figures

It is known that a system which exhibits a half filled lowest flat band and the localized one-particle Wannier states on the flat band satisfy the connectivity conditions, is always ferromagnetic. Without the connectivity conditions on the flat band, the system is non-magnetic. We show that this is not always true. The reason is connected to a peculiar behavior of the band situated just above the flat band., Comment: 15 pages, 4 figures

We model conducting pentagon chains with a multi orbital Hubbard model and prove that well below half filling exact ferromagnetic ground states appear. The rigorous method we use is based on the transformation of original hamiltonian into positive semidefinite form. This technique is independent of the spatial dimesion and does not require integrability of the model. The obtained ferromagnetism is connected to dispersionless bands but in a much broader sense than flat band ferromagnetism requires, where on every site a Hubbard term is present. In our case only a small percentage of, even randomly distributed, sites are only interacting., Comment: 12 pages, 2 figures

Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact 4-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspace ${\cal{S}}$ in which the ground state $|\Psi_g\rangle$ is placed, than deduces $|\Psi_g\rangle$ by exact diagonalization in ${\cal{S}}$. The small subspace is obtained by the repeated application of the Hamiltonian $\hat H$ on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of $\hat H$, till the obtained system of equations closes in itself. The procedure which can be applied in principle at fixed but arbitrary system size and number of particles, is interesting by its own since provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for ${\cal{S}}$. The diagonalization inside ${\cal{S}}$ provides an incomplete image about the low lying part of the excitation spectrum, but provides the exact $|\Psi_g\rangle$. Once the exact ground state is obtained, its properties can be easily analyzed. The $|\Psi_g\rangle$ is found always as a singlet state whose energy, interestingly, saturates in the $U \to \infty$ limit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state present "Zittern" (trembling) characteristics which are absent in 2D square Hubbard systems. Consequently, the manifestation of the local Coulomb repulsion in 2D square and honeycomb types of systems presents differences, which can be a real source in the differences in the many-body behavior., Comment: 35 pages, 21 figures

For a general class of conducting polymers with arbitrary large unit cell and different on-site Coulomb repulsion values on different type of sites, I demonstrate in exact terms the emergence possibility of an upper, interaction created "effective" flat band. This last appears as a consequence of a kinetic energy quench accompanied by a strong interaction energy decrease, and leads to a non-saturated ferromagnetic state. This ordered state clearly differs from the known flat-band ferromagnetism. This is because it emerges in a system without bare flat bands, requires inhomogeneous on-site Coulomb repulsions values, and possesses non-zero lower interaction limits at the emergence of the ordered phase., Comment: 22 pages, 3 figures

We construct a class of exact ground states for correlated electrons on pentagon chains in the high density region and discuss their physical properties. In this procedure the Hamiltonian is first cast in a positive semidefinite form using composite operators as a linear combination of creation operators acting on the sites of finite blocks. In the same step, the interaction is also transformed to obtain terms which require for their minimum eigenvalue zero at least one electron on each site. The transformed Hamiltonian matches the original Hamiltonian through a nonlinear system of equations whose solutions place the deduced ground states in restricted regions of the parameter space. In the second step, nonlocal product wave functions in position space are constructed. They are proven to be unique ground states which describe non-saturated ferromagnetic and correlated half metallic states. These solutions emerge when the strength of the Hubbard interaction $U_i$ is site dependent inside the unit cell. In the deduced phases, the interactions tune the bare dispersive band structure such to develop an effective upper flat band. We show that this band flattening effect emerges for a broader class of chains and is not restricted to pentagon chains. For the characterization of the deduced solutions, uniqueness proofs, exact ground state expectation values for long-range hopping amplitudes and correlation functions are also calculated. The study of physical reasons which lead to the appearance of ferromagnetism has revealed a new mechanism for the emergence of an ordered phase, described here in details (because of lack of space see the continuation in the paper)., Comment: 75 pages, 9 figures

Employing a rigorous theoretical method for the construction of exact many-electron ground states we prove that interactions can be employed to tune a bare dispersive band structure such that it develops a flat band. Thereby we show that pentagon chain polymers with electron densities above half filling may be designed to become ferromagnetic or half metallic., Comment: 11 pages, 3 figures

Using a positive semidefinite operator technique one deduces exact ground states for a zig-zag hexagon chain described by a non-integrable Hubbard model with on-site repulsion. Flat bands are not present in the bare band structure, and the operators $\hat B^{\dagger}_{\mu,\sigma}$ introducing the electrons into the ground state, are all extended operators and confined in the quasi 1D chain structure of the system. Consequently, increasing the number of carriers, the $\hat B^{\dagger}_{\mu,\sigma}$ operators become connected i.e. touch each other on several lattice sites. Hence the spin projection of the carriers becomes correlated in order to minimize the ground state energy by reducing as much as possible the double occupancy leading to a ferromagnetic ground state. This result demonstrates in exact terms in a many-body frame that the conjecture made at two-particle level by G. Brocks et al. [Phys.Rev.Lett.93,146405,(2004)] that the Coulomb interaction is expected to stabilize correlated magnetic ground states in acenes is clearly viable, and opens new directions in the search for routes in obtaining organic ferromagnetism. Due to the itinerant nature of the obtained ferromagnetic ground state, the systems under discussion may have also direct application possibilities in spintronics., Comment: 28 pages, 7 figures. In press at Phil. Mag., special issue dedicated to Jim L. Smith

We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension, requires no integrability of the model, and only demands sufficiently many microscopic parameters in the Hamiltonian which have to fulfill certain relations. The scheme is first employed to construct exact ground state for the diamond Hubbard chain in a magnetic field. These ground states are found to exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior, which can be tuned by changing the magnetic flux, local potentials, or electron density. Detailed proofs of the uniqueness of the ground states are presented. By the same technique exact ground states are constructed for triangle Hubbard chains and a one-dimensional periodic Anderson model with nearest-neighbor hybridization. They permit direct comparison with results obtained by variational techniques for f-electron ferromagnetism due to a flat band in CeRh3B2., Comment: 21 pages, 9 figures. Will be published in the proceedings of YKIS2007 conference (November 2007, Kyoto) as a special issue of Progress of Theoretical Physics Supplement. Fig.6 corrected

The genuine physical reasons explaining the delocalization effect of the Hubbard repulsion U are analyzed. First it is shown that always when this effect is observed, U acts on the background of a macroscopic degeneracy present in a multiband type of system. After this step I demonstrate that acting in such conditions, by strongly diminishing the double occupancy, U spreads out the contributions in the ground state wave function, hence strongly increases the one-particle localization length, consequently extends the one-particle behavior producing conditions for a delocalization effect. To be valuable, the reported results are presented in exact terms, being based on the first exact ground states deduced at half filling in two dimensions for a prototype two band system, the generic periodic Anderson model at finite value of the interaction., Comment: 23 pages, 8 figures. Accepted for publication in Phys. Rev. B

Quadratic operators are used in transforming the model Hamiltonian (H) of one correlated and dispersive band in an unique positive semidefinite form coopting both the kinetic and interacting part of H. The expression is used in deducing exact ground states which are minimum energy eigenstates only of the full Hamiltonian. It is shown in this frame that at half filling, also dispersive bands can provide ferromagnetism in exact terms by correlation effects ., Comment: 7 pages

Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density., Comment: 4 pages, 2 figures

We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works for arbitrary even particle number and lattice sites, is based on explicitly given symmetry adapted base vectors constructed in r-space. The Hamiltonian acting on these states generates a closed system of 85 linear equations providing by its minimum eigenvalue the exact ground state of the system. The presented results, described with the aim to generate further creative developments, not only show how the ground state can be exactly obtained and what kind of contributions enter in its construction, but emphasize further characteristics of the spectrum. On this line i) possible explications are found regarding why weak coupling expansions often provide a good approximation for the Hubbard model at intermediate couplings, or ii) explicitly given low lying energy states of the kinetic energy, avoiding double occupancy, suggest new roots for pairing mechanism attracting decrease in the kinetic energy, as emphasized by kinetic energy driven superconductivity theories., Comment: 37 pages, 18 figures

The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The method is based on the construction in r-space of the different type of orthogonal basis wave vectors which span the subspace of the Hilbert space containing the ground state. In order to do this, we start from the possible microconfigurations of the four particles within the system. These microconfigurations are then rotated, translated and spin-reversed in order to build up the basis vectors of the problem. A closed system of nine analytic linear equations is obtained whose secular equation, by its minimum energy solution, provides the ground state energy and the ground state wave function of the model., Comment: 10 pages, 7 figures

In the case of a two-leg Hubbard ladder we present a procedure which allows the exact deduction of the ground state for the four particle problem in arbitrary large lattice system, in a tractable manner, which involves only a reduced Hilbert space region containing the ground state. In the presented case, the method leads to nine analytic, linear, and coupled equations providing the ground state. The procedure which is applicable to few particle problems and other systems as well is based on an r-space representation of the wave functions and construction of symmetry adapted orthogonal basis wave vectors describing the Hilbert space region containing the ground state. Once the ground state is deduced, a complete quantum mechanical characterization of the studied state can be given. Since the analytic structure of the ground state becomes visible during the use of the method, its importance is not reduced only to the understanding of theoretical aspects connected to exact descriptions or potential numerical approximation scheme developments, but is relevant as well for a large number of potential technological application possibilities placed between nano-devices and quantum calculations, where the few particle behavior and deep understanding are important key aspects to know., Comment: 19 pages, 5 figures

Exact static nondegenerate stripe and checkerboard ground states are obtained in a two-dimensional generalized periodic Anderson model, for a broad concentration range below quarter filling. The random droplet states, also present in the degenerate ground state, are eliminated by extending the Hamiltonian with terms of different physical origin such as dimerization, periodic charge displacements, density waves, or distorsion lines., Comment: 12 pages, 8 figures

We construct a class of exact ground states of three-dimensional periodic Anderson models (PAMs) -- including the conventional PAM -- on regular Bravais lattices at and above 3/4 filling, and discuss their physical properties. In general, the f electrons can have a (weak) dispersion, and the hopping and the non-local hybridization of the d and f electrons extend over the unit cell. The construction is performed in two steps. First the Hamiltonian is cast into positive semi-definite form using composite operators in combination with coupled non-linear matching conditions. This may be achieved in several ways, thus leading to solutions in different regions of the phase diagram. In a second step, a non-local product wave function in position space is constructed which allows one to identify various stability regions corresponding to insulating and conducting states. The compressibility of the insulating state is shown to diverge at the boundary of its stability regime. The metallic phase is a non-Fermi liquid with one dispersing and one flat band. This state is also an exact ground state of the conventional PAM and has the following properties: (i) it is non-magnetic with spin-spin correlations disappearing in the thermodynamic limit, (ii) density-density correlations are short-ranged, and (iii) the momentum distributions of the interacting electrons are analytic functions, i.e., have no discontinuities even in their derivatives. The stability regions of the ground states extend through a large region of parameter space, e.g., from weak to strong on-site interaction U. Exact itinerant, ferromagnetic ground states are found at and below 1/4 filling., Comment: 47 pages, 10 eps figures

We report for the first time exact ground-states deduced for the D=2 dimensional generic periodic Anderson model at finite $U$, the Hamiltonian of the model not containing direct hopping terms for $f$-electrons $(t^f = 0)$. The deduced itinerant phase presents non-Fermi liquid properties in the normal phase, emerges for real hybridization matrix elements, and not requires anisotropic unit cell. In order to deduce these results, the plaquette operator procedure has been generalised to a block operator technique which uses blocks higher than an unit cell and contains $f$-operator contributions acting only on a single central site of the block., Comment: 21 pages, 3 figures

The derivation procedure of exact ground-states for the periodic Anderson model (PAM) in restricted regions of the parameter space and D=2 dimensions using plaquette operators is presented in detail. Using this procedure, we are reporting for the first time exact ground-states for PAM in 2D and finite value of the interaction, whose presence do not require the next to nearest neighbor extension terms in the Hamiltonian. In order to do this, a completely new type of plaquette operator is introduced for PAM, based on which a new localized phase is deduced whose physical properties are analyzed in detail. The obtained results provide exact theoretical data which can be used for the understanding of system properties leading to metal-insulator transitions, strongly debated in recent publications in the frame of PAM. In the described case, the lost of the localization character is connected to the break-down of the long-range density-density correlations rather than Kondo physics., Comment: 34 pages, 5 figures

We report exact multielectronic ground-states dependent on electron concentration for quantum mechanical two-dimensional disordered two-band type many body models in the presence of disordered hoppings and disordered repulsive finite Hubbard interactions, in fixed lattice topology considered provided by Bravais lattices. The obtained ground-states loose their eigenfunction character for independent electron approximation, perturbatively are not connected to the non-interacting but disordered case, and describe a localization-delocalization transition driven by the electron concentration, being highly degenerated and paramagnetic., Comment: Accepted for publication in Phys. Rev. B

We present a class of exact ground states of a three-dimensional periodic Anderson model at 3/4 filling. Hopping and hybridization of d and f electrons extend over the unit cell of a general Bravais lattice. Employing novel composite operators combined with 55 matching conditions the Hamiltonian is cast into positive semidefinite form. A product wave function in position space allows one to identify stability regions of an insulating and a conducting ground state. The metallic phase is a non-Fermi liquid with one dispersing and one flat band., Comment: 4 pages, 3 figures

Presenting exact solutions for the two dimensional periodic Anderson model with finite and nonzero on-site interaction U>0, we are describing a rigorous non-Fermi liquid phase in normal phase and 2D. This new state emerges in multi-band interacting Fermi systems above half filling, being generated by a flat band effect. The momentum distribution function n_k together with its derivatives of any order is continuous. The state possesses a well defined Fermi energy, but the Fermi momentum concept is not definable, so the Fermi surface in k-space is missing. The state emerges in the vicinity of a Mott insulating phase when lattice distortions are present, is highly degenerated and paramagnetic. A gap is present at high U in the density of low lying excitations. During low lying excitations, quasi-particles are not created above the Fermi level, only the number of particles at the Fermi energy increases., Comment: 46 pages, 2 ps files, to be published in Phys. Rev. B

Based on representations of the symmetric group $S_N$, explicit and exact Schr\"odinger equation is derived for $U=\infty$ Hubbard model in any dimensions with arbitrary number of holes, which clearly shows that during the movement of holes the spin background of electrons plays an important role. Starting from it, at T=0 we have analyzed the behaviour of the system depending on the dimensionality and number of holes. Based on the presented formalism thermodynamic quantities have also been expressed using a loop summation technique in which the partition function is given in terms of characters of $S_N$. In case of the studied finite systems, the loop summation have been taken into account exactly up to the 14-th order in reciprocal temperature and the results were corrected in higher order based on Monte Carlo simulations. The obtained results suggest that the presented formalism increase the efficiency of the Monte Carlo simulations as well, because the spin part contribution of the background is automatically taken into account by the characters of $S_N$., Comment: 26 pages, 1 embedded ps figure; Phil. Mag. B (in press)

We present exact results for the periodic Anderson model for finite Hubbard interaction 0 <= U < +infinity on certain restricted domains of the model's phase diagram, in d=1 dimension. Decomposing the Hamiltonian into positive semidefinite terms we find two quantum states to be ground state, an insulating and a metallic one. The ground state energy and several ground state expectation values are calculated., Comment: 10 pages, 4 figures