The Exact Results in the One-dimensional Attractive Hubbard Model

Jakubczyk, Dorota

doi:10.5506/aphyspolb.45.1759

Cited by 5 publications

(6 citation statements)

References 30 publications

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“…The eigenvalues of these blocks can be analytically found by applying the so-called basis of wavelets [60,61] …”

Section: Spin-electron Double-tetrahedral Chainmentioning

confidence: 99%

Magnetization plateau as a result of the uniform and gradual electron doping in a coupled spin-electron double-tetrahedral chain

Gálisová

2017

Phys. Rev. E

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The double-tetrahedral chain in a longitudinal magnetic field, whose nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular plaquettes with the dynamics described by the Hubbard model, is rigorously investigated. It is demonstrated that the uniform change of electron concentration controlled by the chemical potential in a combination with the competition between model parameters and the external magnetic field leads to the formation of one chiral and seven non-chiral phases at the absolute zero temperature. Rational plateaux at onethird and one-half of the saturation magnetization can also be identified in the low-temperature magnetization curves. On the other hand, the gradual electron doping results in eleven different ground-state regions which distinguish from each other by the evolution of the electron distribution during this process. Several doping-dependent magnetization plateaux are observed in the magnetization process as a result of the continuous change of electron content in the model.

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“…The eigenvalues of these blocks can be analytically found by applying the so-called basis of wavelets [60,61] …”

Section: Spin-electron Double-tetrahedral Chainmentioning

confidence: 99%

Magnetization plateau as a result of the uniform and gradual electron doping in a coupled spin-electron double-tetrahedral chain

Gálisová

2017

Phys. Rev. E

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“…For the higher order Green's functions appearing in Eqs. (5) and (6) we will apply irreducible Green's functions technique [26]. In this technique the irreducible part (ir) of the Green's function is defined as…”

Section: The Modelmentioning

confidence: 99%

“…The model expresses dependence between the kinetic energy, Coulomb interactions, and the band structure. It has been analyzed in one-dimensional (1D) systems [3][4][5][6], multi-dimensional, and infinitedimensional systems [7]. Despite its simplicity, Hubbard model has the exact solution only in one-dimensional (1D) systems [3] and for infinite-dimensional systems [7].…”

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confidence: 99%

Modified equation of motion approach for metallic ferromagnetic systems with the correlated hopping interaction

Górski

Mizia

Kucab

2016

Physica Status Solidi (b)

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We consider the extended Hubbard model with included nearest neighbors off‐diagonal correlated hopping interaction. This model is analyzed using the modified equation of motion (EOM) approach with double‐time Green's functions. In modified EOM method we calculate the retarded Green's function of the impurity by differentiating Green's functions over both time variables. The proposed model is used to investigate possibility of ferromagnetism in the itinerant system. We calculate the Curie temperature for different carrier concentrations, state densities with different asymmetry, different values of the Coulomb interaction and correlated hopping interaction. Results of our relatively simple method are compared and agree with the results of previous Quantum Monte Carlo and Modified Perturbation Theory calculations. This legitimates further use of this model in different physical applications, e.g., quantum dots.

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“…For the classical Fibonacci sequence the matrix generators, named as the golden matrix, have the form = [ 1 1 1 0 ] and = [ +1 −1 ], for ≥ 1. Golden number and golden section have many interesting applications in different areas of science (physics, chemistry, and mechanics); see for example [7,8]. In this section we give the matrix generators for distance Fibonacci numbers ( ) ( , ), where = 1, 2, 3.…”

Section: Matrix Generators Andmentioning

confidence: 99%