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Superconductivity, Metastability and Magnetic Field Induced Phase Separation in the Atomic Limit of the Penson-Kolb-Hubbard Model

100%
Kapcia K.
Acta Physica Polonica A
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2014
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vol. 126
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issue 4a
A-53-A-58
EN
We present the analysis of paramagnetic effects of magnetic field (B) (Zeeman term) in the zero-bandwidth limit of the extended Hubbard model for arbitrary chemical potential μ and electron density n. The effective Hamiltonian considered consists of the on-site interaction U and the intersite charge exchange term I, determining the hopping of electron pairs between nearest-neighbour sites. The model has been analyzed within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation (rigorous in the limit of infinite dimensions d → +∞). In this report we focus on metastable phases as well as phase separated states involving superconducting and nonordered phases and determine their ranges of occurrence for U/I_0=1.05 (I_0=zI) in the presence of magnetic field B≠0. Our investigations of the general case for arbitrary U/I_0 show that, depending on the values of interaction parameters (for fixed n), the phase separating state can occur in higher fields than the homogeneous superconducting phase (field-induced phase separated). Moreover, a first-order superconducting-nonordered transition occurs between metastable phases and these metastable phases can exist inside the regions of the phase separated state stability. Such behaviour is associated with the presence of tricritical line on the phase diagrams of the system.
2
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Electron Phase Separations Involving Superconductivity in the Extended Hubbard Models with Pair Hopping Interaction

100%
Kapcia K.
|
EN
In this work the extended Hubbard models with pair hopping interaction (at the atomic limit) are investigated within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation (exact in d → +∞). We analyze mutual stability of the superconducting phase and charge or (ferro/antiferro-)magnetic orderings as well as homogeneous mixed phases. Our preliminary results for U=0 show that the superconducting phase can coexist with the charge or (ferro/antiferro-)magnetic phases only in states with electron phase separation.
3
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Some Properties of the Model of a~Superconductor with Pair Hopping and Magnetic Interactions at Half-Filling

100%
Kapcia K.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
733-737
EN
We present our preliminary studies of an effective model of a superconductor with short coherence length involving magnetic interactions. The Hamiltonian considered consists of (i) the effective on-site interaction U, (ii) the intersite magnetic exchange interactions (J^z, J^{xy}) between nearest-neighbors and (iii) the intersite charge exchange term I, determining the hopping of electron pairs between nearest-neighbor sites. In the analysis of the phase diagrams and thermodynamic properties of this model for half-filling (n=1) we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. One finds that the system considered can exhibit very interesting multicritical behaviors (including tricritical, critical-end and bicritical points) caused by the competition between magnetism and superconductivity, even for n=1. Our investigations show that, depending on the values of interaction parameters, the system at half-filling can exhibit three homogeneous phases: superconducting (SS), (anti-)ferromagnetic (F) and nonordered (NO). The transitions between ordered phases (SS, F) and the NO phase can be first order as well as second order ones, whereas SS-F transition is first order one. Temperature dependencies of the order parameters and thermodynamic properties of the system at the sequence of transitions: SS→F→NO with increasing temperature for J/I=0.3, U/I_0 = 0.69 and n=1 are also presented.
4
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Stable and Metastable Phases in the Atomic Limit of the Extended Hubbard Model with Intersite Density-Density Interactions

64%
Kapcia K., Robaszkiewicz S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 5-6
1029-1031
EN
We have studied a simple effective model of charge ordered insulators. The tight binding Hamiltonian consists of the effective on-site interaction U and the intersite density-density interaction W_{ij} (both: nearest-neighbor and next-nearest-neighbor). In the analysis of the phase diagrams and thermodynamic properties of this model we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigations of the general case (as a function of the electron concentration n) have shown that the system exhibits various critical behaviors including among others bicritical, tricritical, critical-end, and isolated critical points. In this report we concentrate on the metastable phases and transitions between them. One finds that the first- and second order transitions between metastable phases can exist in the system. These transitions occur in the neighborhood of first as well as second order transitions between stable phases. For the case of on-site attraction the regions of metastable homogeneous phases occurrence inside the ranges of phase separated states stability have been also determined.
5
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Phase Separations in the Narrow-Bandwidth Limit of the Penson-Kolb-Hubbard Model at Zero Temperature

64%
Kapcia K., Czart W.
Acta Physica Polonica A
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2018
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vol. 133
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issue 3
401-404
EN
In this work we study the ground state of the Penson-Kolb-Hubard model in the limit of narrow-bandwidth. We present phase diagrams of the model for fixed chemical potential and concentration (involving various phase separations). The results are derived within the Hartree-Fock approximation (HFA) in the narrow-bandwidth regime and compared with the exact ones in the atomic limit and the high-dimension regime. Our investigation reveals that the HFA can reconstruct the exact diagram at the ground state when the bandwidth approaches to zero.
6
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Ground State Phase Diagram of the Extended Hubbard Model with Pair-Hopping Interaction in the Limit of Very Narrow Bandwidth

64%
Kapcia K., Czart W.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
617-620
EN
The extended Hubbard model with the pair-hopping interaction, i.e. the Penson-Kolb-Hubbard model, is one of the conceptually simplest phenomenological models for studying correlations and for description of superconductivity in very narrow-band systems with short-range, almost unretarded pairing. We present ground state phase diagrams of the model derived within the broken-symmetry Hartree-Fock approximation in the narrow-bandwidth regime and compare these results with the exact ones in the atomic limit for the limit of high dimensions. The investigation of the diagrams of the model show that results obtained within both approaches are consistent, although for the case of the finite single-electron hopping phases with magnetic long-range order also occur.
7
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Monte Carlo Study of Phase Separation in Magnetic Insulators

51%
Murawski S., Kapcia K., Pawłowski G., Robaszkiewicz S.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
281-283
EN
In this work we focus on the study of phase separation in the zero-bandwidth extended Hubbard with nearest-neighbors intersite Ising-like magnetic interactions J and on-site Coulomb interactions U. The system has been analyzed by means of the Monte Carlo simulations (in the grand canonical ensemble) on two-dimensional square lattice (with N = L × L = 400 sites) and the results for U/(4J) = 2 as a function of chemical potential and electron concentration have been obtained. Depending on the values of interaction parameters the system exhibits homogeneous (anti-)ferromagnetic or non-ordered phase as well as phase separation state. Transitions between homogeneous phases (i.e. antiferromagnetic-non-ordered transitions) can be of first or second order and the tricritical point is also present on the phase diagrams. The electron compressibility K is an indicator of the phase separation and that quantity is of particular interest of this paper.
8
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Some Exact Results for the Zero-Bandwidth Extended Hubbard Model with Intersite Charge and Magnetic Interactions

51%
Kapcia K., Kłobus W., Robaszkiewicz S.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
284-286
EN
The extended Hubbard model in the zero-bandwidth limit is studied. The effective Hamiltonian consists of (i) on-site U interaction, (ii) intersite density-density interaction W, and (iii) Ising-like magnetic exchange interaction J between the nearest-neighbors. We present rigorous (and analytical) results obtained within the transfer-matrix method for 1D chain in two particular cases: (a) W=0 and n=1; (b) U → +∞ and n=1/2 (W ≠ 0, J ≠ 0). We obtain the exact formulae for the partition functions which enables to calculate thermodynamic properties such as entropy, specific heat (c), and double occupancy per site. In both cases the system exhibits an interesting temperature dependence of c involving a characteristic two-peak structure. There are no phase transitions at finite temperatures and the only transitions occur in the ground state.
9
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Interplay between Charge and Magnetic Orderings in the Zero-Bandwidth Limit of the Extended Hubbard Model for Strong On-Site Repulsion

51%
Kapcia K., Kłobus W., Robaszkiewicz S.
Acta Physica Polonica A
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2012
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vol. 121
|
issue 5-6
1032-1034
EN
A simple effective model of charge ordered and (or) magnetically ordered insulators is studied. The tight binding Hamiltonian analyzed consists of (i) the effective on-site interaction U, (ii) the intersite density-density interaction W and (iii) intersite magnetic exchange interaction J^{z} (or J^{xy}) between nearest-neighbors. The intersite interaction are treated within the mean-field approximation. One shows that the systems considered can exhibit very interesting multicritical behaviors, including among others bicritical, tricritical, tetracritical and critical end points. The analysis of the model has been performed for an arbitrary electron concentration as well as an arbitrary chemical potential in the limit of strong on-site repulsion (U → +∞). The phase diagrams obtained in such a case are shown to consist of at least 9 different states, including four homogeneous phases: nonordered (NO), ferromagnetic (F), charge ordered (CO), ferrimagnetic (intermediate, I) and five types of phase separation: NO-NO, F-NO, F-F, CO-F, CO-I.
10
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On the Phase Diagram of the Zero-Bandwidth Extended Hubbard Model with Intersite Magnetic Interactions for Strong On-Site Repulsion Limit

51%
Murawski S., Kapcia K., Pawłowski G., Robaszkiewicz S.
Acta Physica Polonica A
|
2012
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vol. 121
|
issue 5-6
1035-1037
EN
In this report we have analyzed a simple effective model for a description of magnetically ordered insulators. The Hamiltonian considered consists of the effective on-site interaction (U) and the intersite Ising-like magnetic exchange interaction (J) between nearest neighbors. For the first time the phase diagrams of this model have been determined within Monte Carlo simulation on 2D-square lattice. They have been compared with results obtained within variational approach, which treats the on-site term exactly and the intersite interactions within mean-field approximation. We show within both approaches that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic (F) and nonordered (NO), but also phase separated states (PS: F-NO).
11
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Charge Orderings and Phase Separations in the Atomic Limit of the Extended Hubbard Model with Intersite Density-Density Interactions

51%
Kapcia K., Kłobus W., Robaszkiewicz S.
Acta Physica Polonica A
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2010
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vol. 118
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issue 2
350-352
EN
A simple effective model of charge ordered insulators is studied. The tight binding Hamiltonian consists of the effective on-site interaction U and the intersite density-density interactions W_{ij} (both: nearest-neighbour and next-nearest neighbour). In the analysis of the phase diagrams we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. The phase separated states have not been taken into account in previous analyses. Our investigations of two cases of the on-site interaction: attraction (U/(- W_{Q}) = - 10) and repulsion (U/(- W_{Q}) = 1.1) show that, depending on the values of the next-nearest neighbour attraction, the system can exhibit not only homogeneous phases: charge ordered and nonordered, but also various phase separated states (charge ordered-nonordered, charge ordered-charge ordered).
12
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Magnetic Orderings and Phase Separations in the Zero-Bandwidth Limit of the Extended Hubbard Model with Intersite Magnetic Interactions

51%
Kłobus W., Kapcia K., Robaszkiewicz S.
Acta Physica Polonica A
|
2010
|
vol. 118
|
issue 2
353-355
EN
A simple effective model for a description of magnetically ordered insulators is analysed. The tight binding Hamiltonian consists of the effective on-site interaction (U) and intersite magnetic exchange interactions (J^{z}, J^{xy}) between nearest neighbours. The phase diagrams of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We show that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic (F_α) and nonordered (NO), but also phase separated states (PS_α: F_α-NO).
13
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Some Properties of Two-Dimensional Extended Repulsive Hubbard Model with Intersite Magnetic Interactions - A Monte Carlo Study

51%
Murawski S., Kapcia K., Pawłowski G., Robaszkiewicz S.
Acta Physica Polonica A
|
2014
|
vol. 126
|
issue 4a
A-110-A-114
EN
In this paper the two-dimensional extended Hubbard model with intersite magnetic Ising-like interaction in the atomic limit is analyzed by means of the classical Monte Carlo method in the grand canonical ensemble. Such an effective simple model could describe behavior of insulating (anti)ferromagnets. In the model considered the Coulomb interaction (U) is on-site and the magnetic interactions in z-direction (J>0, antiferromagnetic) are restricted to nearest-neighbors. Simulations of the model have been performed on a square lattice consisting of N=L× L=400 sites (L=20) in order to obtain the full phase diagram for U/(4J)=1. Results obtained for on-site repulsion (U>0) show that, apart from homogeneous non-ordered (NO) and ordered magnetic (antiferromagnetic, AF) phases, there is also a region of phase separation (PS: AF/NO) occurrence. We present a phase diagram as well as some thermodynamic properties of the model for the case of U/(4J)=1 (and arbitrary chemical potential and arbitrary electron concentration). The AF-NO transition can be second-order as well as first-order and the tricritical point occurs on the diagram.
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