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Browsing Artykuły naukowe (WF) by Subject "atomic limit"
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Item Charge orderings and phase separations in the atomic limit of the extended Hubbard model with intersite density-density interactions(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, Pl-02-668 Warsaw, Poland, 2010-08) Kapcia, Konrad; Kłobus, Waldemar; Robaszkiewicz, StanisławWe 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 Wij (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) 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.Item Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas(MDPI, 2021-04-30) Kapcia, Konrad JerzyThe adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to S=1/2 fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite W1 and W2 (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive W1>0, the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state (T=0) diagram for W2≤0 as well as finite temperature (T>0) phase diagrams for W2=0 are presented. Two different types of charge order within √3×√3 unit cell can occur. At T=0, for W2=0 phase separated states are degenerated with homogeneous phases (but T>0 removes this degeneration), whereas attractive W2<0 stabilizes phase separation at incommensurate fillings. For U/W1<0 and U/W1>1/2 only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive 0Item Charge-order on the triangular lattice: Effects of next-nearest-neighbor attraction in finite temperatures(Elsevier, 2021-09-03) Konrad, Jerzy KapciaThe extended Hubbard model in the atomic limit, which is equivalent to lattice S=1/2 fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard U interaction and both nearest-neighbor (W1) and next-nearest-neighbor (W2) density-density intersite interactions. The variational approach treating the $U$ term exactly and the $W_l$ terms in the mean-field approximation is used to investigate thermodynamics of the model and to find its finite temperature (T>0) phase diagrams (as a function of particle concentration) for W1>0 and W2<0. Two different types of charge-order (i.e., DCO and TCO phases) within $\sqrt{3} \times \sqrt{3}$ unit cells as well as the nonordered (NO) phase occur on the diagram. Moreover, several kinds of phase-separated (PS) states (NO/DCO, DCO/DCO, DCO/TCO, and TCO/TCO) are found to be stable for fixed concentration. Attractive W2}<0 stabilizes PS states at T=0 and it extends the regions of their occurrence at T>0. The evolution of the diagrams with increasing of |W2|/W1 is investigated. It is found that some of the PS states are stable only at T>0. Two different critical values of |W2|/W1 are determined for the PS states, in which two ordered phases of the same type (i.e., two domains of the DCO or TCO phase) coexist.Item Electron phase separations involving superconductivity in the extended Hubbard models with pair hopping interaction(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, PL-02-668 Warsaw, Poland, 2015-02) Kapcia, Konrad JerzyIn 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 $d\rightarrow+\infty$). We analyze mutual stability of the superconducting (SC) phase and charge (CO) or (ferro/antiferro-)magnetic (M) orderings as well as homogeneous mixed phases. Our preliminary results for U=0 show that the SC phase can coexist with the CO or M phases only in states with electron phase separation.Item Interplay and competition between superconductivity and charge orderings in the zero-bandwidth limit of the extended Hubbard model with pair hopping and on-site attraction(Springer, 2013-08) Kapcia, KonradWe present studies of an effective model which is a simple generalization of the standard model of a local pair superconductor with on-site pairing (i.e., the model of hard core bosons on a lattice) to the case of finite pair binding energy. The tight binding Hamiltonian consists of (i) the effective on-site interaction U, (ii) the intersite density-density interactions W between nearest-neighbours, and (iii) the intersite charge exchange term I, determining the hopping of electron pairs between nearest-neighbour sites. In the analysis of the phase diagrams and thermodynamic properties of this model we treat the intersite interactions within the mean-field approximation. Our investigations of the U<0 and W>0 case show that, depending on the values of interaction parameters, the system can exhibit three homogeneous phases: superconducting (SS), charge-ordered (CO) and nonordered (NO) as well as the phase separated SS-CO state.Item Interplay between charge and magnetic orderings in the zero-bandwidth limit of the extended Hubbard model for strong on-site repulsion(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, Pl-02-668 Warsaw, Poland, 2012-06) Kapcia, Konrad; Kłobus, Waldemar; Robaszkiewicz, StanisławA 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 Jz (or Jxy) 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. The phase diagrams obtained in such a case are shown to consist of at least 9 different states, including four homogenous 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.Item Magnetic orderings and phase separations in the zero-bandwidth limit of the extended Hubbard model with intersite magnetic interactions(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, Pl-02-668 Warsaw, Poland, 2010-08) Kłobus, Waldemar; Kapcia, Konrad; Robaszkiewicz, StanisławA 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 (Jz, Jxy) 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) and nonordered (NO), but also phase separated states (PS: F-NO).Item Metastability and phase separation in a simple model of a superconductor with extremely short coherence length(Springer US, 233 Spring St, New York, NY 10013 USA, 2014-04) Kapcia, KonradWe present studies of the atomic limit of the extended Hubbard model with pair hopping for arbitrary electron density and arbitrary chemical potential. The Hamiltonian consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange term I, determining the hopping of electron pairs between nearest-neighbour sites. In the analysis of the phase diagrams and thermodynamic properties of this model we treat the intersite interactions within the mean-field approximation. In this report we focus on metastable phases and determine their ranges of occurrence. Our investigations in the absence of the external magnetic field show that the system analysed exhibits tricritical behaviour. Two metastable phases (superconducting and nonordered) can exist inside the regions of the phase separated state stability and a first-order transition occurs between these metastable phases.Item Monte Carlo study of phase separation in magnetic insulators(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, PL-02-668 Warsaw, Poland, 2015-02) Murawski, Szymon; Kapcia, Konrad Jerzy; Pawłowski, Grzegorz; Robaszkiewicz, StanisławIn 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 Monte Carlo simulations (in the grand canonical ensemble) on two dimensional square lattice (with N=LxL=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 (AF) or non-ordered (NO) phase as well as phase separation PS:AF/NO state. Transitions between homogeneous phases (i.e. AF-NO 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.Item On the phase diagram of the zero-bandwidth extended Hubbard model with intersite magnetic interactions for strong on-site repulsion limit(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, Pl-02-668 Warsaw, Poland, 2012-06) Murawski, Szymon; Kapcia, Konrad; Pawłowski, Grzegorz; Robaszkiewicz, StanisławIn 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).Item Phase separation in a lattice model of a superconductor with pair hopping(IOP Publishing Ltd., Temple Circus, Temple Way, Bristol BS1 6BE, England, 2012-05-30) Kapcia, Konrad; Robaszkiewicz, Stanisław; Micnas, RomanWe have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have possibility of transferring. The phase diagrams and thermodynamic properties 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 have also obtained rigorous results for a linear chain (d=1) in the ground state. Moreover, at T=0 some results derived within the random phase approximation (and the spin-wave approximation) for d=2 and d=3 lattices and within the low density expansions for d=3 lattices are presented. Our investigation of the general case (as a function of the electron concentration and as a function of the chemical potential) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases: superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.Item Some exact results for the zero-bandwidth extended Hubbard model with intersite charge and magnetic interactions(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, PL-02-668 Warsaw, Poland, 2015-02) Kapcia, Konrad Jerzy; Kłobus, Waldemar; Robaszkiewicz, StanisławThe extended Hubbard model in the zero-bandwidth limit is studied. The effective Hamiltonian consists of (i) on-site U interaction and intersite (ii) 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) $U\rightarrow+\infty$ and n=1/2 ($W\neq 0$, $J\neq 0$). We obtain the exact formulas 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.Item Some properties of the model of a superconductor with pair hopping and magnetic interactions at half-filling(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, Pl-02-668 Warsaw, Poland, 2012-04) Kapcia, KonradWe 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 (Jz, Jxy) 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/I0 = 0.69 and n=1 are also presented.Item Some properties of two dimensional extended repulsive Hubbard model with intersite magnetic interactions - a Monte Carlo study(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, PL-02-668 Warsaw, Poland, 2014-10) Murawski, Szymon; Kapcia, Konrad Jerzy; Pawłowski, Grzegorz; Robaszkiewicz, StanisławIn 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=LxL=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.Item Stable and metastable phases in the atomic limit of the extended Hubbard model with intersite density-density interactions(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, Pl-02-668 Warsaw, Poland, 2012-06) Kapcia, Konrad; Robaszkiewicz, StanisławWe 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 Wij (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) 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.Item Superconductivity, charge orderings, magnetism, and their phase separations in the ground state of lattice models of superconductor with very short coherence length(Springer US, 233 Spring St, New York, NY 10013 USA, 2015-04) Kapcia, Konrad JerzyWe present the ground state results for lattice models of superconductor (SC) with extremely short coherence length, which also involve the interplay with charge (CO) and (anti-)ferromagnetic orderings. Our preliminary results at zero-temperature (derived by means of the variational approach which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation, exact in $d\rightarrow+\infty$), yields that the SC phase can coexist with the CO or magnetic (M) phases in states with electron phase separation (PS:SC/CO and PS:SC/M, respectively).Item Superconductivity, metastability and magnetic field induced phase separation in the atomic limit of the Penson-Kolb-Hubbard model(Polish Academy of Sciences, Institute of Physics, al. Lotników 32-46, PL-02-668 Warsaw, Poland, 2014-10) Kapcia, Konrad JerzyWe 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 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 (PS) states involving superconducting (SS) and nonordered (NO) phases and determine their ranges of occurrence for U/I0=1.05 (I0=zI) in the presence of magnetic field B. Our investigations of the general case for arbitrary U/I0 show that, depending on the values of interaction parameters (for fixed n), the PS state can occur in higher fields than the homogeneous SS phase (field-induced PS). Moreover, a first-order SS-NO transition occurs between metastable phases and these metastable phases can exist inside the regions of the PS state stability. Such behaviour is associated with the presence of tricritical line on the phase diagrams of the system.Item The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model(IOP Publishing Ltd., Temple Circus, Temple Way, Bristol BS1 6BE, England, 2011-03-16) Kapcia, Konrad; Robaszkiewicz, StanisławWe have studied the extended Hubbard model in the atomic limit. The Hamiltonian analyzed consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case taking into account for the first time the effects of longer-ranged density-density interaction (repulsive and attractive) as well as possible phase separations shows that, depending on the values of the interaction parameters and the electron concentration, the system can exhibit not only several homogeneous charge ordered (CO) phases, but also various phase separated states (CO-CO and CO-nonordered). One finds that the model considered exhibits very interesting multicritical behaviours and features, including among others bicritical, tricritical, critical-end and isolated critical points.Item The magnetic field induced phase separation in a model of a superconductor with local electron pairing(IOP Publishing Ltd., Temple Circus, Temple Way, Bristol BS1 6BE, England, 2013-02-13) Kapcia, Konrad; Robaszkiewicz, StanisławWe have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential and focus on paramagnetic effects of the external magnetic field. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach (VA), which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case shows that the system can exhibit not only the homogeneous phases: superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). Depending on the values of interaction parameters, the PS state can occur in higher fields than the SS phase (field-induced PS). Some ground state results beyond the VA are also presented.