arXiv subjects

S. Kettemann

Publications and source records attributed to S. Kettemann.

At least 19 recordsLinked to original sources

arXiv2026

Machine Learning the Strong Disorder Renormalization Group Method for Disordered Quantum Spin Chains

We train machine learning algorithms to infer the entanglement structure of disordered long-range interacting quantum spin chains by learning from the strong disorder renormalisation group (SDRG) method. The system consists of $S=1/2$-quantum spins coupled by antiferromagnetic power-law interactions with decay exponent $α$ at random positions on a one-dimensional chain. Using SDRG as a physics-informed teacher, we compare a Random Forest classifier as a classical baseline with a graph neural network (GNN) that operates directly on the interaction graph and learns a bond-ranking rule mirroring the SDRG decimation policy. The GNN achieves a disorder-averaged pairing accuracy close to one and reproduces the entanglement entropy $S(\ell)$ in excellent quantitative agreement with SDRG across all subsystem sizes and interaction exponents. RG flow heat maps confirm that the GNN learns the sequential decimation hierarchy rather than merely fitting final-state observables. Finite-temperature entanglement properties are incorporated via the SDRGX framework through a two-stage strategy, using the zero-temperature GNN to generate the RG flow and sampling thermal occupations from the canonical ensemble, yielding results in agreement with both numerical SDRGX and analytical predictions without retraining.

cond-mat.dis-nn↗

arXiv2023

Towards a Comprehensive Theory of Metal-Insulator Transitions in Doped Semiconductors

A review is given on the theory of metal-insulator transitions (MIT) in doped semiconductors. We focus in particular on reviewing theories of their anomalous magnetic properties, which emerge from the interplay of spin and charge correlations and disorder.Building on the review of these existing theories and experiments, we suggest that the finite temperature phase diagram can be structured into 1. a random quantum spin liquid phase at subcritical doping and low temperature, as described by the Bhatt-Lee theory of random spin clusters, mostly random singlets. 2. a critical non-Fermi-liquid fan, originating at the MIT, which is dominated by random Kondo singlets with a universal tail of the distribution of their binding energies. This is caused by multifractality and results in an anomalous power law divergence of the magnetic susceptibility with a universal power and 3. a supercritical, low temperature phase. Rare events caused by the random placement of dopants do not allow to define strict phase boundaries. Remaining open problems are reveiwed and outlined. Finally, the possibility of finite temperature delocalization transitions is reviewed, which arcaused by the correlation induced temperature dependence of the spin scattering rate from magnetic moments. This review article is devoted to the memory of Konstantin B. Efetov.

cond-mat.dis-nn↗

arXiv2021

Inhomogeneous Kondo destruction by RKKY correlations

The competition between the indirect exchange interaction (IEC) of magnetic impurities in metals and the Kondo effect gives rise to a rich quantum phase diagram, the Doniach Diagram. In disordered metals, both the Kondo temperature and the IEC are widely distributed due to the scattering of the conduction electrons from the impurity potential. Therefore, it is a question of fundamental importance, how this Doniach diagram is modified by the disorder, and if one can still identify separate phases. Recently, it has been investigated the effect of Ruderman-Kittel-Kasuya-Yosida (RKKY) correlations on the Kondo effect of two magnetic impurities, renormalizing the Kondo interaction based on the Bethe-Salpeter equation and performing the poor men's renormalization group (RG) analysis with the RKKY-renormalized Kondo coupling. In the present study, we extend this theoretical framework, allowing for different Kondo temperatures of two RKKY-coupled magnetic impurities due to different local exchange couplings and density of states. As a result, we find that the smaller one of the two Kondo temperatures is suppressed more strongly by the RKKY interaction, thereby enhancing their initial inequality. In order to find out if this relevance of inequalities between Kondo temperatures modifies the distribution of the Kondo temperature in a system of a finite density of randomly distributed magnetic impurities, we present an extension of the RKKY coupled Kondo RG equations. We discuss the implication of these results for the interplay between Kondo coupling and RKKY interaction in disordered electron systems and the Doniach diagram in disordered electron systems.

cond-mat.str-el↗

arXiv2020

Spatial BCS-BEC crossover in superconducting p-n junctions

We present a theory of superconducting p-n junctions. We consider a 2-band model of doped bulk semiconductors with attractive interactions between the charge carriers and derive the superconducting order parameter, the quasiparticle density of states and the chemical potential as a function of semiconductor gap $Δ_0$ and the doping level $\varepsilon$. We verify previous results for the quantum phase diagram (QPD) for a system with constant density of states in the conduction and valence band, which show BCS-Superconductor to Bose-Einstein-Condensation (BEC) and BEC to Insulator transitions as function of doping level and band gap. Then, we extend it to a 3D density of states and derive the QPD, finding that a BEC phase can only exist for small band gaps $Δ_0 < Δ_0^*$. For larger band gaps, there is a direct transition from an insulator to a BCS phase. Next, we apply this theory to study the properties of superconducting p-n junctions, deriving the spatial variation of the superconducting order parameter along the p-n junction. We find a spatial crossover between a BCS and BEC condensate, as the density of charge carriers changes across the p-n junction. For the 2D system, we find two regimes, when the bulk is in a BCS phase, a BCS-BEC-BCS junction with a single BEC layer, and a BCS-BEC-I-BEC-BCS junction with two layers of BEC condensates separated by an insulating layer. In 3D there can also be a conventional BCS-I-BCS junction for semiconductors with band gaps exceeding $Δ_0^*$. Thus, there can be BEC layers in the well controlled setting of doped semiconductors, where the doping level can be varied to change the thickness of BEC layers, making Bose Einstein Condensates possibly accessible to experimental transport and optical studies in solid state materials.

cond-mat.supr-con↗

arXiv2017

Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

We investigate the magnetic susceptibility $χ(T)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic coupling as a function of their spatial decay exponent $α$ and cutoff length $ξ$. The calculations are based on the strong disorder renormalization method which is used to obtain the temperature dependence of $χ(T)$ and distribution functions of couplings at each renormalization step. For the case with only algebraic decay ($ ξ= \infty$) we find a crossover at $α^*=1.066$ between a phase with a divergent low-temperature susceptibility $χ(T\rightarrow 0) $ for $α> α^*$ to a phase with a vanishing $χ(T\rightarrow 0) $ for $α< α^*$. For finite cutoff lengths $ξ$, this crossover occurs at a smaller $α^*(ξ)$. Additionally we study the localization of spin excitations for $ ξ= \infty$ by evaluating the distribution function of excitation energies and we find a delocalization transition that coincides with the opening of the pseudo-gap at $α_c=α^*$.

cond-mat.dis-nn↗

arXiv2016

Delocalization of Phase Disturbances and the Stability of AC Electricity Grids

The energy transition towards an increased supply of renewable energy raises concerns that existing electricity grids, built to connect few centralized large power plants with consumers, may become more difficult to control and stabilized with a rising number of decentralized small scale generators. Here, we aim to study therefore, how local phase perturbations which may be caused by local power fluctuations, affect the AC grid stability. To this end, we start from nonlinear power balance equations and map them to complex linear wave equations, yielding stationary solutions with phases $φ_i$ at generator and consumer sites $i$. Next, we study deviations from these stationary solutions. Starting with an initially localized perturbation, it is found to spread in a periodic grid diffusively throughout the grid. We derive the parametric dependence of diffusion constant $D$. We apply the same solution strategy to general grid topologies and analyse their stability against local perturbations. The perturbation remains either localized or becomes delocalized, depending on grid topology, power capacity and distribution of consumers and generators $P_i$. Delocalization is found to increase the lifetime of perturbations and thereby their influence on grid stability, while localization results in an exponentiallyfast decay of perturbations at all grid sites. These results may therefore lead to new strategies to control the stability of electricity grids.

nlin.CD↗

arXiv2015

Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions

While there are well established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power $α$, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing $α$. At $α_c$ the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many body localization transition in disordered antiferromagnetic spin chains with long range interactions.

cond-mat.dis-nn↗

arXiv2012

RKKY Interactions in Graphene: Dependence on Disorder and Gate Voltage

We report the dependence of Ruderman-Kittel-Kasuya-Yoshida\,(RKKY) interaction on nonmagmetic disorder and gate voltage in grapheme. First the semiclassical method is employed to reserve the expression for RKKY interaction in clean graphene. Due to the pseudogap at Dirac point, the RKKY coupling in undoped grapheme is found to be proportional to $1/R^3$. Next, we investigate how the RKKY interaction depends on nonmagnetic disorder strength and gate voltage by studying numerically the Anderson tight-binding model on a honeycomb lattice. We observe that the RKKY interaction along the armchair direction is more robust to nonmagnetic disorder than in other directions. This effect can be explained semiclassically: The presence of multiple shortest paths between two lattice sites in the armchair directions is found to be responsible for the reduceddisorder sensitivity. We also present the distribution of the RKKY interaction for the zigzag and armchair directions. We identify three different shapes of the distributions which are repeated periodically along the zigzag direction, while only one kind, and more narrow distribution, is observed along the armchair direction. Moreover, we find that the distribution of amplitudes of the RKKY interaction crosses over from a non-Gaussian shape with very long tails to a completely log-normal distribution when increasing the nonmagnetic disorder strength. The width of the log-normal distribution is found to linearly increase with the strength of disorder, in agreement with analytical predictions. At finite gate voltage near the Dirac point, Friedel oscillation appears in addition to the oscillation from the interference between two Dirac points. This results in a beating pattern. We study how these beating patterns are effected by the nonmagnetic disorder in doped graphene.

cond-mat.mes-hall↗

arXiv2012

Kondo-Anderson Transitions

Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical Power law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature $T_{K}$ is derived at the AMIT, in the metallic phase and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field $B$ and at finite temperature $T$. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as function of temperature. We find a phase diagram with finite temperature transitions between insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions (KATs).

cond-mat.str-el↗

arXiv2011

RKKY Interaction in Disordered Graphene

We investigate the effects of nonmagnetic disorder on the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction in graphene by studying numerically the Anderson model with on-site and hopping disorder on a honeycomb lattice at half filling. We evaluate the strength of the interaction as a function of the distance R between two magnetic ions, as well as their lattice positions and orientations. In the clean limit, we find that the strength of the interaction decays as 1/R^3, with its sign and oscillation amplitude showing strong anisotropy. With increasing on-site disorder, the mean amplitude decreases exponentially at distances exceeding the elastic mean free path. At smaller distances, however, the oscillation amplitude increases strongly and its sign changes on the same sublattice for all directions but the armchair direction. For random hopping disorder, no sign change is observed. No significant changes to the geometrical average values of the RKKY interaction are found at small distances, while exponential suppression is observed at distances exceeding the localization length.

cond-mat.mes-hall↗

arXiv2010

Dimensional Dependence of Weak Localization Corrections and Spin Relaxation in Quantum Wires with Rashba Spin-Orbit Coupling

The quantum correction to the conductivity in disordered quantum wires with linear Rashba spin-orbit coupling is obtained. For quantum wires with spin-conserving boundary conditions, we find a crossover from weak anti- to weak localization as the wire width W is reduced using exact diagonalization of the Cooperon equation. This crossover is due to the dimensional dependence of the spin relaxation rate of conduction electrons, which becomes diminished, when the wire width is smaller than the bulk spin precession length $L_{SO}$. We thus confirm previous results for small wire width, $W/L_{SO}<= 1$ [PRL98,176808(2007)], where only the transverse 0-modes of the Cooperon equation had been taken into account. We find that spin helix solutions become stable for arbitrary ratios of linear Rashba and Dresselhaus coupling in narrow wires. For wider wires, the spin relaxation rate is found to be not monotonous as function of wire width: it becomes first enhanced for W on the order of the bulk $L_{SO}$ before it becomes diminished for smaller wire widths. In addition, we find that the spin relaxation is smallest at the edge of the wire for wide wires. The effect of the Zeeman coupling to the magnetic field perpendicular to the 2D electron system is studied and found that it shifts the crossover from weak anti- to weak localization to larger wire widths $W_c$. When the transverse confinement potential of the quantum wire is smooth (adiabatic), the spin relaxation rate is found to be enhanced as W is reduced. We find that only a spin polarized state retains a finite spin relaxation rate in such narrow wires. Thus, we conclude that the injection of polarized spins into nonmagnetic quantum wires should be favorable in wires with smooth confinement potential. Finally, in wires with tubular shape, corresponding to transverse periodic boundary conditions, we find no reduction of the spin relaxation rate.

cond-mat.mes-hall↗

arXiv2009

Critical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities

It is well-known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo screening is strongly suppressed. We find that when the exchange coupling J is smaller than a certain value J*, the metal-insulator transition point extends to a critical region in the disorder strength parameter and to a band of critical states. The width of this critical region increases with a power of the concentration of magnetic impurities.

cond-mat.str-el↗

arXiv2007

Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals

The crossover between a free magnetic moment phase and a Kondo phase in low dimensional disordered metals with dilute magnetic impurities is studied. We perform a finite size scaling analysis of the distribution of the Kondo temperature as obtained from a numerical renormalization group calculation of the local magnetic susceptibility and from the solution of the self-consistent Nagaoka-Suhl equation. We find a sizable fraction of free (unscreened) magnetic moments when the exchange coupling falls below a disorder-dependent critical value $J_{\rm c}$. Our numerical results show that between the free moment phase due to Anderson localization and the Kondo screened phase there is a phase where free moments occur due to the appearance of random local pseudogaps at the Fermi energy whose width and power scale with the elastic scattering rate $1/τ$.

cond-mat.str-el↗

arXiv2007

Dimensional Control of Antilocalisation and Spin Relaxation in Quantum Wires

The spin relaxation rate $1/τ_s (W)$ in disordered quantum wires with Rashba and Dresselhaus spin-orbit coupling is derived analytically as a function of wire width $W$. It is found to be diminished when $W$ is smaller than the bulk spin-orbit length $L_{\rm SO}$. Only a small spin relaxation rate due to cubic Dresselhaus coupling $γ$ is found to remain in this limit. As a result, when reducing the wire width $W$ the quantum conductivity correction changes from weak anti- to weak localization and from negative to positive magnetoconductivity.

cond-mat.mes-hall↗

arXiv2005

Random Network Models and Quantum Phase Transitions in Two Dimensions

An overview of the random network model invented by Chalker and Coddington, and its generalizations, is provided. After a short introduction into the physics of the Integer Quantum Hall Effect, which historically has been the motivation for introducing the network model, the percolation model for electrons in spatial dimension 2 in a strong perpendicular magnetic field and a spatially correlated random potential is described. Based on this, the network model is established, using the concepts of percolating probability amplitude and tunneling. Its localization properties and its behavior at the critical point are discussed including a short survey on the statistics of energy levels and wave function amplitudes. Magneto-transport is reviewed with emphasis on some new results on conductance distributions. Generalizations are performed by establishing equivalent Hamiltonians. In particular, the significance of mappings to the Dirac model and the two dimensional Ising model are discussed. A description of renormalization group treatments is given. The classification of two dimensional random systems according to their symmetries is outlined. This provides access to the complete set of quantum phase transitions like the thermal Hall transition and the spin quantum Hall transition in two dimension. The supersymmetric effective field theory for the critical properties of network models is formulated. The network model is extended to higher dimensions including remarks on the chiral metal phase at the surface of a multi-layer quantum Hall system.

cond-mat.mes-hall↗

arXiv2005

A Spin-Mechanical Device for Detection and Control of Spin Current by Nanomechanical Torque

We propose a spin-mechanical device to control and detect spin currents by mechanical torque. Our hybrid nano-electro-mechanical device, which contains a nanowire with a ferromagnetic-nonmagnetic interface, is designed to measure or induce spin polarized currents. Since spin carries angular momentum, a spin flip or spin transfer process involves a change in angular momentum--and hence, a torque--which enables mechanical measurement of spin flips. Conversely, an applied torque can result in spin polarization and spin current.

cond-mat.mes-hall↗

arXiv2004

Distribution of the Kondo Temperature in Mesoscopic Disordered Metals

The Kondo temperature of a magnetic impurity in a weakly disordered metal is distributed due to the randomness in the local exchange coupling, and the local electronic density of states (LDOS). We show that in a closed, phase coherent metal particle the resulting distribution of $T_K$ is strongly asymmetric and scales with the mean level spacing $Δ$. Its width is $2 \sqrt{Δ/βT_K}$, where $Δ$ is the mean level spacing, and $β=1,2$, with, without time reversal symmetry, respectively. Increasing the density of magnetic impurities, the distribution of Kondo temperatures (DKT) is found to become more narrow. Corrections to these results due to Anderson localisation are discussed.

cond-mat.mes-hall↗

arXiv2004

The Mesoscopic Quantum-Hall-Insulator Transition

Sharp localization transitions of chiral edge states in disordered quantum wires, subject to strong magnetic field, are shown to be driven by crossovers from two- to one-dimensional localization of bulk states. As a result, the two-terminal conductance is found to exhibit at zero temperature discontinuous transitions between {\it exactly} integer plateau values and zero, reminiscent of first order phase transitions. We discuss the corresponding phase diagram. The spin of the electrons is shown to result in a multitude of phases, when the spin degeneracy is lifted by the Zeeman energy. The width of conductance plateaus is found to depend sensitively on the spin flip rate $1/τ_s$.

cond-mat.mes-hall↗