arXiv subjects

Václav Janiš

Publications and source records attributed to Václav Janiš.

At least 19 recordsLinked to original sources

arXiv2026

A microscopic theory of Anderson localization of electrons in random lattices

The existence of Anderson localization, characterized by vanishing diffusion due to strong disorder, has been demonstrated in numerous ways. A systematic approach based on the Anderson quantum model of the Fermi gas in random lattices that can describe both diffusive and localized regimes has not yet been fully established. We build on a recent publication \cite{Janis:2025ab} and present a microscopic theory of disordered electrons that covers both the metallic phase with extended Bloch waves and the localized phase, where a propagating particle forms a quantum bound state with the hole left behind at the origin. The general theory provides a framework for constructing controlled approximations to one- and two-particle Green functions that satisfy the necessary conservation laws and causality requirements across the full range of disorder strength. It is used explicitly to derive a local, mean-field-like approximation for the two-particle irreducible vertices, enabling quantitative analysis of the solution's dynamic properties in both metallic and localized phases, including critical behavior at the mobility edge. A new instability line for the dynamical electron-hole correlation function of the metallic phase is introduced.

cond-mat.dis-nn↗

arXiv2025

Quantum dynamics in symmetry-breaking states of correlated electrons: Antiferromagnetic phase

Symmetry-breaking phases in many-fermion systems are characterized by anomalous functions that represent transient processes during which some properties of free particles, such as spin or charge, are not conserved. Connecting the low-temperature symmetry-breaking phase with the high-temperature one within the Baym-Kadanoff scheme, beyond the static mean-field approximation, remains an unresolved, long-standing challenge. We identify the reason why approximations with critical dynamical fluctuations in the Schwinger-Dyson equation lead to a mismatch in the transition temperatures calculated from the high- and low-temperature phases. We propose a solution to this generic problem by excluding anomalous contributions to response functions that do not obey conservation of excitations in their interactions. We illustrate this behavior using the example of an antiferromagnetic state. We reveal that the spectral function in the antiferromagnetic phase exhibits a double-gap structure at zero temperature when the anomalous self-energy is frequency-dependent.

cond-mat.str-el↗

arXiv2025

Anderson localization: A disorder-induced quantum bound state

Electrons at the Fermi energy may lose their ability to propagate to long distances in certain random media. We use Green functions and solve parquet equations for the non-local electron-hole vertex in high spatial dimensions to describe the vanishing of diffusion in Anderson localization. It is caused by forming a quantum bound state between the diffusing particle and the hole left behind. Divergence in a new time scale proportional to the electrical polarizability signals the Anderson localization transition. Consequently, the height of the peak of the dynamical conductivity at zero frequency, the static diffusion constant, is not pushed to zero at the localization transition but rather its width. Spatially localized quantum bound states in the localized phase cannot be described by the continuity and wave equations in the Hilbert space of Bloch waves.

cond-mat.dis-nn↗

arXiv2024

Failure of the Baym-Kadanoff construction to match consistently quantum dynamics with thermodynamic critical behavior

We disclose a serious deficiency of the Baym-Kadanoff construction of thermodynamically consistent conserving approximations. There are two vertices in this scheme: dynamical and conserving. The divergence of each indicates a phase instability. We show that each leads to incomplete and qualitatively different behavior at different critical points. The diagrammatically controlled dynamical vertex from the Schwinger-Dyson equation does not obey the Ward identity and cannot be continued beyond its singularity. The standardly used dynamical vertex alone cannot, hence, conclusively decide about the stability of the high-temperature phase. On the other hand, the divergence in the conserving vertex, obeying the conservation laws, does not invoke critical behavior of the spectral function and the specific heat. Moreover, the critical behavior of the conserving vertex may become spurious in low-dimensional systems. Consequently, the description of the critical behavior of correlated electrons becomes consistent and reliable only if the fluctuations of the order parameter in the conserving vertex lead to a divergence coinciding with that of the dynamical one.

cond-mat.str-el↗

arXiv2023

Orientational ordering of water molecules confined in beryl: A theoretical study

We present an improved model for studying the interactions between dipole moments of water molecules confined in beryl crystals, inspired by recent NMR experiments. Our model is based on a local crystal potential with dihexagonal symmetry for the rotations of water dipole moments, leading to deflection from the $ab$ hexagonal crystallographic plane. This potential shape has significant implications for dipole ordering, which is linked to the non-zero projection of the dipole moment on the hexagonal $c$ axis. To reveal the tendency toward equilibrium-ordered states, we used a variational mean-field approximation, Monte Carlo simulations, and quantum tunneling. Our analysis reveals three types of equilibrium-ordered states: a purely planar dipole order with an antiparallel arrangement in the adjacent planes, a configuration with deflected dipole moments ordered in antiparallel directions, and a helical structure of the dipoles twisting along the $c$ axis.

cond-mat.mtrl-sci↗

arXiv2021

Failure of the mean-field description of magnetic fluctuations in the superconducting quantum dot

The zero-temperature physics of interacting quantum dots attached to superconducting leads is now well understood. The overall qualitative picture is obtained from the static mean-field approximation. The situation drastically changes at non-zero temperatures. No reliable solutions apart from numerical simulations exist there. We show that any static mean-field approximation fails at non-zero temperatures since magnetic fluctuations induce dynamical corrections that lead to broadening of the in-gap state energies to energy bands. Spin-symmetric equilibrium state at non-zero temperatures is unstable with respect to magnetic fluctuations and the zero magnetic field can be reached only as a weak limit of the spin-polarized solution like in a magnetically ordered phase.

cond-mat.str-el↗

arXiv2021

Single impurity Anderson model out of equilibrium: A two-particle semi-analytic approach

We apply a two-particle semi-analytic approach to a single Anderson impurity attached to two biased metallic leads. The theory is based on reduced parquet equations justified in critical regions of singularities in the Bethe-Salpeter equations. It offers a way to treat one-particle and two-particle thermodynamic and spectral quantities on the same footing. The two-particle vertices are appropriately renormalized so that spurious transitions into the magnetic state of the weak-coupling approximations are suppressed. The unphysical hysteresis loop in the current-voltage characteristics is thereby eliminated. Furthermore, in the linear response regime, we qualitatively reproduce the three transport regimes with the increasing temperature: from the Kondo resonant tunneling through the Coulomb blockade regime up to a sequential tunneling regime. Far from equilibrium, we find that the bias plays a similar role as the temperature in destroying the Kondo resonant peak when the corresponding energy scale is comparable with the Kondo temperature. Besides that, the applied voltage in low bias is shown to develop spectral peaks around the lead chemical potentials as observed in previous theoretical and experimental studies.

cond-mat.str-el↗

arXiv2021

Green functions in the renormalized many-body perturbation theory

I review the way the many-body Green functions are used to renormalize the perturbation theory of correlated fermions. The Green functions are introduced to implement systematically dynamical corrections to the static mean-field theory. The renormalizations enter the perturbation theory via self-consistent evaluations of one-particle and two-particle Green functions. The one-particle self-consistency is discussed within the Baym-Kadanoff construction. We point to an inherent dichotomy of the Baym-Kadanoff approach in the relation between one and two-particle Green functions. They are the Schwinger-Dyson equation, directly derived from the generating Luttinger-Ward functional, and the Ward identity. The latter imposes a severe restriction on the two-particle irreducible vertex and is not guaranteed in the Baym-Kadanoff approach. No approximate theory is capable to obey both relations. I further discuss the two-particle approach with two-particle renormalizations that offers a way to reconcile the Schwinger-Dyson equation and the Ward identity. The two-particle irreducible vertex from the critical Bethe-Salpeter equation becomes a generating functional in the two-particle renormalization of the perturbation theory. The irreducible vertex is used in the Ward identity to determine the order parameter beyond the critical point and in the Bethe-Salpeter equation representing the vertex of the Schwinger-Dyson equation to determine the spectral self-energy in such a way that the thermodynamic critical behavior from both equations is qualitatively the same. Finally, I discuss a static mean-field-like approximation with a renormalized effective interaction determined self-consistently that leads to a qualitatively correct description of strong electron correlations in impurity and lattice models.

cond-mat.str-el↗

arXiv2021

Dynamical Mean-Field Theory of Disordered Electrons: Coherent Potential Approximation and Beyond

I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body systems by using many-body Green functions. The many-body approach is used to derive the coherent-potential approximation and to show how it fits into the dynamical mean-field theory. The generating functional of the coherent-potential approximation is obtained in an analytic form from the limit to infinite dimensions of the general many-body description of non-interacting electrons in random lattices. The analytic generating functional of the mean-field description of random systems is extended to the Falicov-Kimball model with thermally equilibrated scattering lattice potential. The many-body Green functions are then used to calculate transport properties. The electrical conductivity of the coherent-potential approximation is derived from the two-particle Green function calculated in infinite spatial dimensions. Finally, a perturbation theory for the vertex corrections to the mean-field conductivity is introduced. In particular, it is shown how to make the expansion beyond the local approximations conserving.

cond-mat.dis-nn↗

arXiv2021

Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic field

We develop the general many-body perturbation theory for a superconducting quantum dot represented by a single-impurity Anderson model attached to superconducting leads. We build our approach on a thermodynamically consistent mean-field approximation with a two-particle self-consistency of the parquet type. The two-particle self-consistency leading to a screening of the bare interaction proves substantial for suppressing the spurious transitions of the Hartree-Fock solution. We demonstrate that the magnetic field plays a fundamental role in the extension of the perturbation theory beyond the weakly correlated $0$-phase. It controls the critical behavior of the $0-π$ quantum transition, lifts the degeneracy in the $π$-phase, where the limits to zero temperature and zero magnetic field do not commute. The response to the magnetic field is quite different in $0$- and $π$-phases. While the magnetic susceptibility vanishes in the $0$-phase it becomes of the Curie type and diverges in the $π$-phase at zero temperature.

cond-mat.str-el↗

arXiv2020

Antiferromagnetic fluctuations in the one-dimensional Hubbard model

We study the low-temperature critical behavior of the one-dimensional Hubbard model near half filling caused by enhanced antiferromagnetic fluctuations. We use a mean-field-type approximation with a two-particle self-consistency renormalizing the bare interaction. It allows us to control a transition from high to low temperatures as well as from weak to strong-coupling. We show that there is a crossover temperature $T_{0}= t\exp\{-1/Uρ(0)\}$ for arbitrary interaction $U>0$ and the bare density of states at the Fermi energy $ρ(0)>0$. The solution at lower temperatures goes over to strong coupling and approaches a quantum critical point with the diverging staggered susceptibility and a gap in the excitation spectrum at zero temperature.

cond-mat.str-el↗

arXiv2020

Curie-Weiss susceptibility in strongly correlated electron systems

The genesis of the Curie-Weiss magnetic response observed in most transition metals that are Fermi liquids at low temperatures has been an enigma for decades and has not yet been fully explained from microscopic principles. We show on the single-impurity Anderson model how the quantum dynamics of strong electron correlations leads to the Curie-Weiss magnetic susceptibility sufficiently above the Kondo temperature. Such behavior has not yet been demonstrated and can be observed only when the bare interaction is substantially screened (renormalized) and a balance between quantum and thermal fluctuations is kept. We set quantitative criteria for the existence of the Curie-Weiss law.

cond-mat.str-el↗

arXiv2019

Kondo Temperature and High to Low Temperature Crossover in Quantum Dots

Kondo temperature is standardly defined from the local zero-temperature susceptibility in the regime of strong electron correlations as a new scale controlling the low-temperature asymptotics of thermodynamic quantities. We show by using a two-particle self-consistent theory that the Kondo temperature can be identified as a crossover temperature at which the zero-temperature quantum fluctuations equal the thermal ones in the electron-hole correlation function. The high-temperature Curie-Weiss susceptibility is shown to go over to the Pauli one below the Kondo temperature.

cond-mat.str-el↗

arXiv2019

Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency

A two-particle self-consistency is rarely part of mean-field theories. It is, however, essential for avoiding spurious critical transitions and unphysical behavior. We present a general scheme for constructing analytically controllable approximations with self-consistent equations for the two-particle vertices based on the parquet equations. We explain in detail how to reduce the full set of parquet equations not to miss quantum criticality in strong coupling. We further introduce a decoupling of convolutions of the dynamical variables in the Bethe-Salpeter equations to make them analytically solvable. We connect the self-energy with the two-particle vertices to satisfy the Ward identity and the Schwinger-Dyson equation. We discuss the role of the one-particle self-consistency in making the approximations reliable in the whole spectrum of the input parameters. We demonstrate the general construction on the simplest static approximation that we apply to the Kondo behavior of the single-impurity Anderson model.

cond-mat.str-el↗

arXiv2017

Mean-field approximation for thermodynamic and spectral functions of correlated electrons: Strong-coupling and arbitrary band filling

We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced parquet equations. It is a static local approximation of the two-particle irreducible vertex, the kernel of a potentially singular Bethe-Salpeter equation. The effective interaction enters the Ward identity from which a thermodynamic self-energy, renormalizing the one-electron propagators, is determined. The dynamical Schwinger-Dyson equation with the thermodynamic propagators is then used to calculate the spectral properties. The thermodynamic and spectral properties of correlated electrons are in this way determined on the same footing and in a consistent manner. Such a mean-field approximation is analytically controllable and free of unphysical behavior and spurious phase transitions. We apply the construction to the asymmetric Anderson impurity and the Hubbard models in the strong-coupling regime.

cond-mat.str-el↗

arXiv2017

Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure

We study the subgap spectrum of the interacting single-level quantum dot coupled between two superconducting reservoirs, forming the Josephson-type circuit, and additionally hybridized with a metallic normal lead. This system allows for the phase-tunable interplay between the correlation effects and the proximity-induced electron pairing resulting in the singlet-doublet (0-$π$) crossover and the phase-dependent Kondo effect. We investigate the spectral function, induced local pairing, Josephson supercurrent, and Andreev conductance in a wide range of system parameters by the numerically exact Numerical Renormalization Group and Quantum Monte Carlo calculations along with perturbative treatments in terms of the Coulomb repulsion and the hybridization term. Our results address especially the correlation effects reflected in dependencies of various quantities on the local Coulomb interaction strength as well as on the coupling to the normal lead. We quantitatively establish the phase-dependent Kondo temperature $\log T_{K}(ϕ)\propto\cos^{2}(ϕ/2)$ and show that it can be read off from the half-width of the zero-bias enhancement in the Andreev conductance in the doublet phase, which can be experimentally measured by the tunneling spectroscopy.

cond-mat.mes-hall↗

arXiv2016

Thermodynamically consistent description of criticality in models of correlated electrons

Criticality in models of correlated electrons emerges in proximity of a low-temperature singularity in a two-particle Green function. Such singularities are generally related to a symmetry breaking of the one-particle self-energy. A consistent description demands that the symmetry breaking in the self-energy emerges at the critical point of the respective two-particle function. This cannot easily be achieved in models of correlated electrons, since there are two ways connecting one- and two-electron functions that cannot be made fully equivalent in approximations. We present a general construction of diagrammatic two-particle approximations consistent with the one-particle functions so that both produce qualitatively the same quantum critical behavior in thermodynamically equivalent descriptions. The general scheme is applied on the single-impurity Anderson model to derive qualitatively the same Kondo critical scale from the spectral function and the magnetic susceptibility.

cond-mat.str-el↗

arXiv2016

Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads

Self-consistent perturbation expansion up to the second order in the interaction strength is used to study a single-level quantum dot with local Coulomb repulsion attached asymmetrically to two generally different superconducting leads. At zero temperature and wide range of other parameters the spin-symmetric version of the expansion yields excellent results for the position of the $0-π$ impurity quantum phase transition boundary and Josephson current together with the energy of Andreev bound states in the $0$-phase as confirmed by numerical calculations using the Numerical Renormalisation Group method. We analytically prove that the method is charge-conserving as well as thermodynamically consistent. Explicit formulas for the position of the $0-π$ phase boundary are presented for the Hartree-Fock approximation as well as for its variant called Generalized Atomic Limit. It is shown that the Generalized Atomic Limit can be used as a quick estimate for the position of the phase boundary at half-filling in a broad range of parameters. We apply our second order perturbation method to the interpretation of the existing experimental data on the phase boundary with very satisfactory outcome suggesting that the so far employed heavy numerical tools such as Numerical Renormalization Group and/or Quantum Monte Carlo are not necessary in a class of generic situations and can be safely replaced by a perturbative approach.

cond-mat.mes-hall↗