arXiv subjects

Krzysztof Byczuk

Publications and source records attributed to Krzysztof Byczuk.

At least 37 records · Page 2Linked to original sources

arXiv2008

Influence of Band and Orbital Degeneracies on Ferromagnetism in the Periodic Anderson Model

We investigate the influence of degeneracies of the conduction band and the $f$-orbital on the stability of ferromagnetism in the periodic Anderson model. To this end we calculate the temperature dependence of the inverse susceptibility for different degeneracies $D^c, D^f$ and conduction electron densities $n^c$ within the dynamical mean-field theory. A strong increase of the Curie temperature $T_c$ with the degeneracy $D^f$ of the localized $f$-level is found. For $D^c \leq D^f$ a simple \emph{ansatz} based on a mean-field treatment of the RKKY interaction is shown to imply a scaling behavior of $T_c$ as a function of the conduction electron density per band which is well obeyed by the numerical results. In particular, $T_c$ is found to have a maximum at $n^c / D^c\approx 0.3$.

cond-mat.str-el↗

arXiv2008

Competition between Anderson localization and antiferromagnetism in correlated lattice fermion systems with disorder

The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically different to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.

cond-mat.str-el↗

arXiv2008

Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases

We formulate a bosonic dynamical mean-field theory (B-DMFT) which provides a comprehensive, thermodynamically consistent framework for the theoretical investigation of correlated lattice bosons. The B-DMFT is applicable for arbitrary values of the coupling parameters and temperature and becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In contrast to its fermionic counterpart the construction of the B-DMFT requires different scalings of the hopping amplitudes with Z depending on whether the bosons are in their normal state or in the Bose-Einstein condensate. A detailed discussion of how this conceptual problem can be overcome by performing the scaling in the action rather than in the Hamiltonian itself is presented. The B-DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. It reproduces all previously investigated limits in parameter space such as the Beliaev-Popov and Hartree-Fock-Bogoliubov approximations and generalizes the existing mean-field theories of interacting bosons. The self-consistency equations of the B-DMFT are those of a bosonic single-impurity coupled to two reservoirs corresponding to bosons in the condensate and in the normal state, respectively. We employ the B-DMFT to solve a model of itinerant and localized, interacting bosons analytically. The local correlations are found to enhance the condensate density and the Bose-Einstein condensate (BEC) transition temperature T_{BEC}. This effect may be used experimentally to increase T_{BEC} of bosonic atoms in optical lattices.

cond-mat.other↗

arXiv2008

Ferromagnetism and Kondo Insulator Behavior in the Disordered Periodic Anderson Model

The effect of binary alloy disorder on the ferromagnetic phases of f-electron materials is studied within the periodic Anderson model. We find that disorder in the conduction band can drastically enhance the Curie temperature due to an increase of the local f-moment. The effect may be explained qualitatively and even quantitatively by a simple theoretical ansatz. The emergence of an alloy Kondo insulator at non-integer filling is also pointed out.

cond-mat.str-el↗

arXiv2005

Local moment approach to multi-orbital single impurity Anderson model; application to dynamical mean-field theory

Using a local moment approach of Logan et al. we developed a solver for a multi-orbital single impurity Anderson model. The existence of the local moments is taken from the outset and their values are determined through variational principle by minimizing the corresponding ground state energy. The method is used to solve the dynamical mean-field equations for the multi-orbital Hubbard model. In particular, the Mott-Hubbard metal--insulator transition is addressed within this approach.

cond-mat.str-el↗

arXiv2005

Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.

cond-mat.str-el↗

arXiv2005

Mott--Hubbard and Anderson Transitions in Dynamical Mean--Field Theory

The Anderson--Hubbard Hamiltonian at half--filling is investigated within dynamical mean--field theory at zero temperature. The local density of states is calculated by taking the geometric and arithmetic mean, respectively. The non--magnetic ground state phase diagrams obtained within the different averaging schemes are compared.

cond-mat.str-el↗

arXiv2004

Metal--Insulator Transitions in the Falicov--Kimball Model with Disorder

The ground state phase diagrams of the Falicov--Kimball model with local disorder is derived within the dynamical mean--field theory and using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases are identified. The metal--insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.

cond-mat.str-el↗

arXiv2004

Curie temperature and quantum phase transitions in the Hubbard model with binary alloy disorder

Magnetic and electric properties of the Hubbard model with binary alloy disorder are studied within the dynamical mean--field theory. A paramagnet--ferromagnet phase transition and a Mott--Hubbard metal--insulator transition are observed upon varying the alloy concentration. A disorder induced enhancement of the Curie temperature is demonstrated and explained by the effects of band splitting and subband filling. Different quantum phase transitions driven by changes of the alloy concentration are identified.

cond-mat.str-el↗

arXiv2004

Mott--Hubbard transition vs. Anderson localization of correlated, disordered electrons

The phase diagram of correlated, disordered electrons is calculated within dynamical mean--field theory using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases, as well as coexistence and crossover regimes are identified. The Mott and Anderson insulators are found to be continuously connected.

cond-mat.str-el↗

arXiv2004

What is between Fermi-Dirac and Bose-Einstein Statistics?

We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution function interpolates continuously between the Fermi-Dirac and the Bose-Einstein limits. We present an explicit solution of the transcendental equation for the didtribution function in a general case, as well as determine the thermodynamic properties in both low- and high-temperature limits.

cond-mat.str-el↗

arXiv2003

Mott-Hubbard metal-insulator transition at non-integer filling

Correlated electrons in a binary alloy $A_{x}B_{1-x}$ are investigated within the Hubbard model and dynamical mean--field theory (DMFT). The random energies $ε_{i}$ have a bimodal probability distribution and an energy separation $Δ$. We solve the DMFT equations by the numerical renormalization group method at zero temperature, and calculate the spectral density as a function of disorder strength $Δ$ and interaction $U$ at different fillings. For filling factors $ν=x$ or $1+x$ the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal--insulator transition hysteresis is observed. We also analyze the effective theory in the $Δ\to \infty $ limit and find good agreement between analytical and numerical results for the critical interaction $U_{c}$ at which the metal--insulator transition occurs.

cond-mat.str-el↗

arXiv2002

Ferromagnetism and Metal-Insulator Transition in the Disordered Hubbard Model

A detailed study of the paramagnetic to ferromagnetic phase transition in the one-band Hubbard model in the presence of binary alloy disorder is presented. The influence of the disorder (with concentration $x$ and $1-x$ of the two alloy ions) on the Curie temperature $T_{c}$ is found to depend strongly on electron density $n$. While at high densities, $n>x$, the disorder always reduces $T_c$, at low densities, $n<x$, the disorder can even \emph{enhance} $T_c$ if the interaction is strong enough. At the particular density $n=x$ (i. e. not necessarily at half filling) the interplay between disorder-induced band splitting and correlation induced Mott transition gives rise to a new type of metal-insulator transition.

cond-mat.str-el↗

arXiv2002

Theory of superconducting fluctuations in the thinest carbon nanotubes

The low-energy electronic Hamiltonian for the thinest zigzag carbon nanotube, embedded into a dielectric host, is derived and its phase diagram is discussed. The specific multi-band structure and the microscopic form of the electron-electron interaction in this systems is considered. The interband repulsive interaction, which is almost unscreened, leads to a retarded intraband attraction between the electrons and can stabilize the Cooper pairs. For a dielectric constant of the host $ε_d\sim 2-4$, the theory predicts that the superconducting fluctuations should develop, which is in agreement with the experiment. For $ε_d \gtrsim 8$, the density wave fluctuations should be amplified. Between the two phases, there is a metallic state where all two-particle fluctuations are suppressed.

cond-mat.supr-con↗

arXiv2002

Phenomenological Modeling of Photoemission Spectra in Strongly Correlated Electron Systems

A phenomenological approach is presented that allows one to model, and thereby interpret, photoemission spectra of strongly correlated electron systems. A simple analytical formula for the self-energy is proposed. This self-energy describes both coherent and incoherent parts of the spectrum (quasiparticle and Hubbard peaks, respectively). Free parameters in the expression are determined by fitting the density of states to experimental photoemission data. An explicit fitting is presented for the La$_{1-x}$Sr$_x$TiO$_3$ system with $0.08 \le x \le 0.38$. In general, our phenomenological approach provides information on the effective mass, the Hubbard interaction, and the spectral weight distribution in different parts of the spectrum. Limitations of this approach are also discussed.

cond-mat.str-el↗

arXiv2001

Derivation of the Curie-Weiss Law in Dynamical Mean-Field Theory

We present an analytic derivation of the linear temperature dependence of the inverse static susceptibility $χ^{-1}(T,U)\sim T-T{_{c}}(U)$ near the transition from a paramagnetic to a ferromagnetic correlated metal within the dynamical mean-field theory (DMFT) for the Hubbard model. The equations for the critical temperature and interaction strength of the transition are also determined.

cond-mat.str-el↗

arXiv1999

Spin configurations of carbon nanotube in a nonuniform external potential

We study, theoretically, the ground state spin of a carbon nanotube in the presence of an external potential. We find that when the external potential is applied to a part of the nanotube, its variation changes the single electron spectrum significantly. This, in combination with Coulomb repulsion and the symmetry properties of a finite length armchair nanotube induces spin flips in the ground state when the external potential is varied. We discuss the possible application of our theory to recent measurements of Coulomb blocked peaks and their dependence on a weak magnetic field in armchair carbon nanotubes.

cond-mat.mes-hall↗

arXiv1995

Transition temperature and a spatial dependence of the superconducting gap for multilayer high-temperature superconductors

We derive the expressions for the transition temperature $(T_{c})$, and the spatial dependence of the superconducting gap for a multilayer high-$T_{c}$ superconductor composed of groups of tightly spaced planes separated by a larger distance. The results are compared with experiment and provide a strong support for an interlayer hopping as the driving force of the large $T_{c}$ enhancement in multilayered compounds. Our results are universal in the sense that they are valid for an arbitrary pairing potential $V_{\bf k k'}$ in the $\rm CuO_{2}$ planes, as well as for both Fermi and nonFermi liquids.

cond-mat↗