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We deduct conditions for the Hamiltonian coupling strengths necessary to achieve flat bands in polymers (i.e. a pentagon chain) considering many-body spin-orbit coupling and external magnetic field. We consider itinerant electrons on pentagon chains with first neighbour hoppings, on-site electron potentials and spin-flip first neighbour hoppings representing the Rashba type spin-orbit interaction (SOI). The external magnetic field is also present in the system via the Peierls phase factors. The band structure is obtained by solving the secular equation of the diagonalized one particle part of the Hamiltonian in k-space (momentum-space). The flat band conditions make the bands k-independent, providing a highly a degenerate state, which gives broad possibilities for applications. In our work we have shown how the SOI is able to relax the strict, rigid flat band conditions given by the Hamiltonian coupling strengths. The role of the external magnetic field was also investigated. [ABSTRACT FROM AUTHOR]

The ferromagnetism of Au nanograins is analyzed 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. [ABSTRACT FROM AUTHOR]

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 details. Casting the Hamiltonian in positive semidefinite form, the technique leads to the ground state, and also characterises the low lying excitation spectrum. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 an exact 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, produce marked changes of the phase diagram. We exemplify this by deducing ferromagnetic ground states in the presence of external fields in two different domains of the parameter space. [ABSTRACT FROM PUBLISHER]

Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact four-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspacein which the ground stateis placed, than deducesby exact diagonalization in. The small subspace is obtained by the repeated application of the Hamiltonianon a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of, 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 on its own since it provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for. The diagonalization insideprovides an incomplete image of the low lying part of the excitation spectrum, but provides the exact. Once the exact ground state is obtained, its properties can be easily analysed. Theis found always as a singlet state whose energy, interestingly, saturates in thelimit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state presents ‘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 behaviour. [ABSTRACT FROM AUTHOR]

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 dimension 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. [ABSTRACT FROM AUTHOR]

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 Ui 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 detail. This works as follows: starting from a completely dispersive bare band structure, the interactions quench the kinetic energy, hence the ordered phase is obtained solely by a drastic decrease of the interaction energy. Since Ui are site dependent, this determinative decrease is obtained by a redistribution of the double occupancy di such to attain small di where the on-site Coulomb repulsion Ui is high, and vice versa. The kinetic energy quench leads to the upper effective flat band, whose role is to enhance by its degeneracy the switching to the ordered phase dictated and stabilized by the interactions present. It is shown that for this phenomenon to occur, a given degree of complexity is needed for the chain, and the mechanism becomes inactive when the Ui interactions are homogeneous, or are missing from the ground state wave function. [ABSTRACT FROM AUTHOR]

A technique based on the transformation in positive semidefinite form of the Hamiltonian (Ĥ) is developed to allow the study of the enlargement possibilities of the emergence domain of a given state. For this reason the calculation of exact ground states for the polyphenylene type of non-integrable chains is performed. Using different exact transcriptions of Ĥ in positive semidefinite form and different solutions of the matching equations, the same type of ground state is deduced in different regions of the parameter space, hence a more global view of its emergence possibilities is obtained. With this procedure an enlarged view of the appearance in the phase diagram of different studied phases can be achieved. [ABSTRACT FROM PUBLISHER]

Using a positive semidefinite operator technique we deduce 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 [image omitted], introducing the electrons into the ground state, are all extended operators and confined in the quasi-1D chain structure of the system. Consequently, by increasing the number of carriers, the [image omitted] 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 the two-particle level by G. Brocks et al., [Phys. Rev. 93 (2004) p.146405.] that the Coulomb interaction is expected to stabilize correlated magnetic ground states in acenes, is clearly viable, and opens up 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 also have direct application possibilities in spintronics. [ABSTRACT FROM AUTHOR]

Explicitly given, exact, ground-state solutions are reported for the one-dimensional periodic Anderson model in the limit of strong on-site repulsion, at and above half-filling, in the generic case of the model, for which f-electron hopping is forbidden. The description is presented for Bravais lattices, and the deduction procedure is based on decomposition of the starting Hamiltonian in positive semidefinite operators, which are defined as combinations of fermionic operators acting on the lattice sites of blocks. In comparison with the previously used procedures of this type, we use blocks greater than a unit cell, and a nonlinear combination of fermionic operators acting on the lattice sites. Based on such block operators, the previously known exact, ground-state solution possibilities at one-quarter and three-quarter filling have been extended to half-filling. The deduced ground state is present in restricted regions of the T = 0 phase diagram of the model, and is a spin-singlet conducting state. [ABSTRACT FROM AUTHOR]

We present exact results for the T = 0 ground state of the t-J model in one dimension in the low-concentration limit and arbitrary coupling constants. The procedure is based on the construction of the ground-state wavefunction in real space by the enumeration of the possible local particle configurations and taking into account the translational and rotational invariance of the system. Concrete results are presented for two- and four-particle cases. [ABSTRACT FROM AUTHOR]

We present exact results for the periodic Anderson model for finite Hubbard interaction 0 < U < ∞ 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 states; a completely localized ground state and a non-localized ground state. The ground-state energy and several ground-state expectation values were calculated. [ABSTRACT FROM AUTHOR]

We present an efficient Monte Carlo method to study the properties of the infinitely repulsive Hubbard model with few holes at finite non-zero temperatures. Using this method, magnetic and specific heat results are presented for a 10 × 10 lattice with two holes. Our results show that the magnetization increases with decreasing temperature for such a finite system. [ABSTRACT FROM AUTHOR]

A foreword to "Philosophical Magazine" is presented.

Discusses the staging of the Second International Summer School on Strongly Correlated Systems in Debrecen, Hungary on September 4-9, 2000, at the Department of Theoretical Physics, University of Debrecen. Changes in academic life; Preparation for the integration process; Financial support for a School for Doctor of Philosophy students; Lectures presented.