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1
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Lattice Green Functions on a Two-Dimensional Rectangular Lattice with Next-Nearest Neighbor Interaction

100%
Bak M.
|
|
issue 2
386-388
EN
The analytic formula for the on-site Green function on the two-dimensional rectangular lattice is shown for arbitrary energy, both within the band (complex Green function) and outside the band (real Green function), expressed by means of elliptic integrals. The recursion formulae enabling calculation of the Green functions on other lattice sites are shown.
2
Content available remote

Critical Values for Electron Pairing in t-U-J-V and t-J-V Models

100%
Bak M.
Acta Physica Polonica A
|
2008
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vol. 114
|
issue 1
275-279
EN
The critical values for pairing of s*- and d-wave symmetry are calculated within the t-U-J-V and the t-J-V models in renormalized mean field theory. It is shown that the first model yields the proper critical values in the low density limit while the other does not. Renormalized mean field theory strongly decreases the absolute value of (negative) critical values for larger electron densities.
3
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Content available

Properties of the Bound States on a Hexagonal Lattice

100%
Bak M.
Acta Physica Polonica A
|
2007
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vol. 111
|
issue 5
781-789
EN
Two electrons on a lattice pose an interesting problem which can be solved exactly. When the effective interactions are strong enough, the bound states are formed. The properties of such bound pairs in an extended Hubbard model are examined for both signs of nearest neighbor hopping integral t. The stabilization of s*-wave pairing is found for t<0 and of f-wave for t>0. Phase diagrams for the existence of none, one or two s*-wave solutions are calculated.
4
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Content available

Universal Relations in the Attractive Hubbard Model with Next-Nearest Neighbor Hopping

100%
Bak M.
Acta Physica Polonica A
|
2006
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vol. 109
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issue 4-5
565-568
EN
Recently a new universal relation between superfluid densityρ_s andσ_{dc}T_c, where σ_{dc} is direct current conductivity and T_c - superconducting critical temperature, was found by Homes et al. (Nature 430, 539 (2004)). The theoretical derivation of the relation based on BCS theory is correct only qualitatively. In the present paper this relation is calculated theoretically, using Hartree-Fock approximation and second-order perturbation theory. It is found that although correct qualitatively, quantitatively the results are too small. Inclusion of the second neighbor hopping improves the results.
5
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S-Wave Bound- and Resonant States of Two Fermions in Simple Cubic Lattice

100%
Bak M.
Acta Physica Polonica A
|
2012
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vol. 121
|
issue 4
808-811
EN
Resonant two-electron states are examined in attractive Hubbard model on simple cubic lattice and exact formula for scattering cross section in the limit of low density (empty lattice) is calculated. S-wave pair is considered by means of lattice Green functions (LGF). Analytical form of these functions found by Joyce is used facilitating calculations, which were greatly hindered before by the necessity of using LGF's tabulated values. It is found that the actual peak of scattering cross-section is formed on the lower band boundary in discrepancy with formulae of the theory of scattering in solids.
6
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Effective Mass of Bound and Resonant Two-Electron Pairs in a Simple Cubic Lattice

100%
Bak M.
Acta Physica Polonica A
|
2015
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vol. 127
|
issue 2
290-292
EN
Effective masses m* of bound 2-electron pairs on a simple cubic lattice were investigated within tUWJ model within symmetry channels. Linear increase of m* with |W| for intersite pairs and nonlinear behavior and sign change of m* in case of pairs with on-site component were found. |m*| turned out to be larger than twice free electron mass.
7
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The Fock Term in the Charge Ordered Phase of the t-W Model

100%
Bak M.
Acta Physica Polonica A
|
2012
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vol. 121
|
issue 5-6
1085-1088
EN
The paper shows the importance of retaining Hartree and Fock terms, appearing after mean-field decoupling, in the treatment of charge ordered phase of the t-W model, with implications to extended Hubbard model.
8
Content available remote

Resonant Two-Electron Pairs in a Simple Cubic Lattice

100%
Bak M.
|
EN
The properties of resonant two-electron pairs are examined in three-dimensional simple cubic extended Hubbard tUW model, in s- and d- symmetry channels, in the limit of empty lattice. Lattice Green function technique is applied to calculate the scattering amplitude by means of 𝓣 matrix for any energy in the band on ΓR line within the Brillouin zone. The analysis shows the persistence of resonant states even for Coulomb interactions so weak that the equation for the resonant states is not formally fulfilled. The difference in behavior of resonances controlled by on-site and intersite Coulomb interactions is found. The ranges of applicability of approximate formula for the actual position of resonant peak and its width are shown.
9
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Mixed State in t-U-J-V Model

64%
Tobijaszewska B., Bak M.
Acta Physica Polonica A
|
2009
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vol. 115
|
issue 1
135-137
EN
The t-U-J-V model in the U → ∞ limit is treated by renormalized mean-field theory for arbitrary electron density. Superconductivity of s+id symmetry is found in the large parts of the phase diagram. Calculations also show a possibility of phase separation.
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