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Register a new userExact ferromagnetic ground state of pentagon chains
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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.
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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).
We use the matrix product approach to construct all optimum ground states of general anisotropic spin-2 chains with nearest neighbour interactions and common symmetries. These states are exact ground states of the model and their properties depend on up to three parameters. We find three different antiferromagnetic Haldane phases, one weak antiferromagnetic and one weak ferromagnetic phase. The antiferromagnetic phases can be described as spin liquids with exponentially decaying correlation functions. The variety of phases found with the matrix product ansatz also gives insight into the behaviour of spin chains with arbitrary higher spins.
We investigate the ground state magnetization plateaus appearing in spin 1/2 polymerized Heisenberg chains under external magnetic fields. The associated fractional quantization scenario and the exponents which characterize the opening of gapful excitations are analyzed by means of abelian bosonization methods. Our conclusions are fully supported by the extrapolated results obtained from Lanczos diagonalizations of finite systems.
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 $|Psi_grangle$ is placed, than deduces $|Psi_grangle$ 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 $|Psi_grangle$. Once the exact ground state is obtained, its properties can be easily analyzed. The $|Psi_grangle$ 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.
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.
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