Browsing by Author "Kapcia, Konrad Jerzy"
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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 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 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 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 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 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 Thermodynamic and electromagnetic properties of the eta--pairing superconductivity in the Penson-Kolb model(Elsevier, 2021-09-06) Czart, Wojciech Robert; Kapcia, Konrad Jerzy; Micnas, Roman; Robaszkiewicz, StanisławIn the paper, we study the thermodynamic and electromagnetic properties of the Penson-Kolb (PK) model, i.e., the tight-binding model for fermionic particles with the pair-hopping interaction J. We focus on the case of repulsive J (i.e., J<0), which can stabilize the eta-pairing superconductivity with Cooper-pair center-of-mass momentum $\vec{q}=\vec{Q}$, $\vec{Q}=(\pi/a$,$\pi/a$,\ldots). Numerical calculations are performed for several d-dimensional hypercubic lattices: d=2 (the square lattice, SQ), d=3 (the simple cubic lattice) and $d=\infty$ hypercubic lattice (for arbitrary particle concentration 00 as a function of n and pairing strength. The analysis of the effects of the Fock term on the ground state phase boundaries and on selected PK model characteristics is performed as well as the influence of the phase fluctuations on the eta-pairing superconductivity is investigated. Within the Kosterlitz-Thouless scenario, the critical temperatures Tkt are estimated for d=2 SQ lattice and compared with the critical temperature Tc obtained from HFA. We also determine the temperature Tm at which minimal gap between two quasiparticle bands vanishes in the eta-phase. Our results for repulsive J are contrasted with those found earlier for the PK model with attractive J (i.e., with J>0).