V. Janis - Academia.edu (original) (raw)

Papers by V. Janis

Ceskoslovensky Casopis pro Fyziku, 2007

physica status solidi (b), 1986

ABSTRACT

Electron Correlations and Materials Properties, 1999

Advances in Solid State Physics

International Journal of Modern Physics B, 1997

We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite inte... more We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite interval to the X-ray edge problem. Dyson equations for basic Green functions from the X-ray problem are rewritten as convolutive integral equations on a time-interval [0,t] with t→∞. The long-time asymptotics of solutions to these equations is derived with the aid of the Wiener–Hopf method. Although the Wiener–Hopf long-time exponents differ by a factor of two from the solution of Nozières and De Dominicis we demonstrate how the latter and the critical exponents of measurable amplitudes from the X-ray problem can be derived from the former. We explain that the difference in the exponents arises due to different ways of performing the long-time limit in the two solutions. To enable the infinite-time limit in the defining equations a new infinite-time scale τ→∞, interpreted as an effective lifetime of the core-hole, must be introduced. The ratio t/τ decides about the resulting critical expone...

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model.... more We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida-Thouless instability line in the nonzero magnetic field.

The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagr... more The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical regions of singularities in the two-particle vertex. The scale vanishing at the critical point defines the Kondo temperature at which the electron-hole correlation function saturates. We show that the Kondo temperature exists at any filling of the impurity level. A quasiparticle resonance peak in the spectral function, however, forms only in almost electron-hole symmetric situations. We relate the Kondo temperature with the width of the resonance peak. Finally we discuss the existence of satellite Hubbard bands in the spectral function.

arXiv: Disordered Systems and Neural Networks, 2015

We address the problem of vanishing of diffusion in noninteracting disordered electron systems an... more We address the problem of vanishing of diffusion in noninteracting disordered electron systems and its description by means of averaged Green functions. Since vanishing of diffusion, Anderson localization, cannot be identified by means of one-electron quantities, one must appropriately approximate two-particle functions. We show how to construct nontrivial and self-consistent approximations for irreducible vertices and to handle them so that the full dynamical Ward identity and all macroscopic conservation laws are obeyed. We derive an approximation-free low-energy representation of the full two-particle vertex that we use to calculate the critical part of the electron-hole correlation function, the diffusion pole and the dynamical diffusion constant. We thereby pave the way for a systematic and controllable description of vanishing of diffusion in disordered systems.

We present a detailed, quantitative study of the competition between interaction- and disorder-in... more We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Anderson-Hubbard model with diagonal disorder is investigated analytically and by Quantum Monte Carlo techniques in the limit of infinite spatial dimensions at half filling. We construct the magnetic phase diagram and find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A novel strong coupling anomaly, i.e.~an {\it increase} of the N\'{e}el-temperature for increasing disorder, is discovered and explained as an generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phase. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.

The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a clo... more The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the free energy as a functional of order parameters. Then we set stationarity equations for local maxima of the free energy determining the order-parameter function on interval [0,1]. Finally we show without resorting to the replica trick that the solution of the stationarity equations leads to a marginally stable thermodynamic state.

AIP Conference Proceedings

We study the single-impurity Anderson model with diagrammatic techniques. We employ the parquet a... more We study the single-impurity Anderson model with diagrammatic techniques. We employ the parquet approach to determine the electron-hole and electron-electron irreducible vertices self-consistently. We demonstrate that when the dominant contributions from the critical region of the singularity driven by multiple electron-hole scatterings are properly taken into account we make the parquet equations soluble and recover the Kondo asymptotics in the symmetric as well as in the asymmetric cases.

Journal of Physics C: Solid State Physics, 1987

ABSTRACT

The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. ... more The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. In this limit the coupled Bethe-Salpeter equations determining two-particle vertices (parquet equations) reduce to a single algebraic equation for a local vertex. We find a disorder-driven bifurcation point in this equation signaling vanishing of electron diffusion and onset of Anderson localization. There is no bifurcation in d=1,2 where all states are localized. In dimensions d>=3 the mobility edge separating metallic and insulating phase is found for various types of disorder and compared with results of other treatments.

Physica B: Condensed Matter, 1996

Two methods, Fredholm and Wiener-Hopf, for solving the microscopic model of the X-ray edge singul... more Two methods, Fredholm and Wiener-Hopf, for solving the microscopic model of the X-ray edge singularity due to Mahan [Phys. Rev. 163 (1967) 612] and Nozières and De Dominicis [Phys. Rev. 178 (1969) 1097] are compared. We analyze the conditions under which these methods deliver a unique (exact) solution. Two large (infinite) time scales must be introduced to distinguish the methods, relaxation time T and an effective lifetime of the excited electron hole pair tau. It is shown that the edge behavior depends on the ratio T/tau being zero in the Fredholm and infinity in the Wiener Hopf approach.

Ceskoslovensky Casopis pro Fyziku, 2007

physica status solidi (b), 1986

ABSTRACT

Electron Correlations and Materials Properties, 1999

Advances in Solid State Physics

International Journal of Modern Physics B, 1997

We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite inte... more We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite interval to the X-ray edge problem. Dyson equations for basic Green functions from the X-ray problem are rewritten as convolutive integral equations on a time-interval [0,t] with t→∞. The long-time asymptotics of solutions to these equations is derived with the aid of the Wiener–Hopf method. Although the Wiener–Hopf long-time exponents differ by a factor of two from the solution of Nozières and De Dominicis we demonstrate how the latter and the critical exponents of measurable amplitudes from the X-ray problem can be derived from the former. We explain that the difference in the exponents arises due to different ways of performing the long-time limit in the two solutions. To enable the infinite-time limit in the defining equations a new infinite-time scale τ→∞, interpreted as an effective lifetime of the core-hole, must be introduced. The ratio t/τ decides about the resulting critical expone...

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model.... more We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida-Thouless instability line in the nonzero magnetic field.

The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagr... more The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical regions of singularities in the two-particle vertex. The scale vanishing at the critical point defines the Kondo temperature at which the electron-hole correlation function saturates. We show that the Kondo temperature exists at any filling of the impurity level. A quasiparticle resonance peak in the spectral function, however, forms only in almost electron-hole symmetric situations. We relate the Kondo temperature with the width of the resonance peak. Finally we discuss the existence of satellite Hubbard bands in the spectral function.

arXiv: Disordered Systems and Neural Networks, 2015

We address the problem of vanishing of diffusion in noninteracting disordered electron systems an... more We address the problem of vanishing of diffusion in noninteracting disordered electron systems and its description by means of averaged Green functions. Since vanishing of diffusion, Anderson localization, cannot be identified by means of one-electron quantities, one must appropriately approximate two-particle functions. We show how to construct nontrivial and self-consistent approximations for irreducible vertices and to handle them so that the full dynamical Ward identity and all macroscopic conservation laws are obeyed. We derive an approximation-free low-energy representation of the full two-particle vertex that we use to calculate the critical part of the electron-hole correlation function, the diffusion pole and the dynamical diffusion constant. We thereby pave the way for a systematic and controllable description of vanishing of diffusion in disordered systems.

We present a detailed, quantitative study of the competition between interaction- and disorder-in... more We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Anderson-Hubbard model with diagonal disorder is investigated analytically and by Quantum Monte Carlo techniques in the limit of infinite spatial dimensions at half filling. We construct the magnetic phase diagram and find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A novel strong coupling anomaly, i.e.~an {\it increase} of the N\'{e}el-temperature for increasing disorder, is discovered and explained as an generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phase. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.

The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a clo... more The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the free energy as a functional of order parameters. Then we set stationarity equations for local maxima of the free energy determining the order-parameter function on interval [0,1]. Finally we show without resorting to the replica trick that the solution of the stationarity equations leads to a marginally stable thermodynamic state.

AIP Conference Proceedings

We study the single-impurity Anderson model with diagrammatic techniques. We employ the parquet a... more We study the single-impurity Anderson model with diagrammatic techniques. We employ the parquet approach to determine the electron-hole and electron-electron irreducible vertices self-consistently. We demonstrate that when the dominant contributions from the critical region of the singularity driven by multiple electron-hole scatterings are properly taken into account we make the parquet equations soluble and recover the Kondo asymptotics in the symmetric as well as in the asymmetric cases.

Journal of Physics C: Solid State Physics, 1987

ABSTRACT

The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. ... more The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. In this limit the coupled Bethe-Salpeter equations determining two-particle vertices (parquet equations) reduce to a single algebraic equation for a local vertex. We find a disorder-driven bifurcation point in this equation signaling vanishing of electron diffusion and onset of Anderson localization. There is no bifurcation in d=1,2 where all states are localized. In dimensions d>=3 the mobility edge separating metallic and insulating phase is found for various types of disorder and compared with results of other treatments.

Physica B: Condensed Matter, 1996

Two methods, Fredholm and Wiener-Hopf, for solving the microscopic model of the X-ray edge singul... more Two methods, Fredholm and Wiener-Hopf, for solving the microscopic model of the X-ray edge singularity due to Mahan [Phys. Rev. 163 (1967) 612] and Nozières and De Dominicis [Phys. Rev. 178 (1969) 1097] are compared. We analyze the conditions under which these methods deliver a unique (exact) solution. Two large (infinite) time scales must be introduced to distinguish the methods, relaxation time T and an effective lifetime of the excited electron hole pair tau. It is shown that the edge behavior depends on the ratio T/tau being zero in the Fredholm and infinity in the Wiener Hopf approach.