arXiv subjects

Stefan Kettemann

Publications and source records attributed to Stefan Kettemann.

At least 19 recordsLinked to original sources

arXiv2026

Probing the Spacetime Structure of Entanglement in Monitored Quantum Circuits with Graph Neural Networks

Global entanglement in quantum many-body systems is inherently nonlocal, raising the question of whether it can be inferred from local observations. We investigate this problem in monitored quantum circuits, where projective measurements generate classical records distributed across spacetime. Using graph neural networks (GNNs), we represent individual quantum trajectories as directed spacetime graphs and reconstruct the half-chain entanglement entropy from local measurement data alone. Because information propagates through the network via local message passing, the architecture directly controls the spacetime region over which correlations can be aggregated. By systematically varying this accessible scale -- through network depth and hierarchical spacetime coarse-graining -- we probe how much measurement information is required to reconstruct global entanglement. We find that prediction accuracy improves as the accessible spacetime region grows and that results from different architectures collapse when expressed in terms of an effective spacetime scale combining depth and coarse-graining. These results demonstrate that the information required to reconstruct global entanglement is organized in spacetime scales and show that graph-based learning architectures provide a controlled operational framework for probing how global quantum correlations emerge from local measurement data.

cond-mat.dis-nn↗

arXiv2025

Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Excited States and Finite Temperature Properties

We extend the recently introduced strong disorder renormalization group method in real space, well suited to study bond disordered antiferromagnetic power law coupled quantum spin chains, to study excited states, and finite temperature properties. First, we apply it to a short range coupled spin chain, which is defined by the model with power law interaction, keeping only interactions between adjacent spins. We show that the distribution of the absolute value of the couplings is the infinite randomness fixed point distribution. However, the sign of the couplings becomes distributed, and the number of negative couplings increases with temperature $T.$ Next, we derive the Master equation for the power law long range interaction between all spins with power exponent $α$. While the sign of the couplings is found to be distributed, the distribution of the coupling amplitude is given by the strong disorder distribution with finite width $2α,$ with small corrections for $α>2$. Resulting finite temperature properties of both short and power law long ranged spin systems are derived, including the magnetic susceptibility, concurrence and entanglement entropy.

cond-mat.dis-nn↗

arXiv2025

Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties

We introduce and implement a reformulation of the strong disorder renormalization group method in real space, well suited to study bond disordered antiferromagnetic power law coupled quantum spin chains. We derive the Master equations for the distribution function of pair distances $\tilde{r}$. First, we apply it to a short range coupled spin chain, keeping only interactions for adjacent spins. We confirm that it is solved by the infinite randomness fixed point distribution. Then, we solve the Master equation for the power law long range interaction between all spins for any anisotropy ranging from the XX-limit to the isotropic Heisenberg limit, corresponding to a tight binding chain of disordered long range interacting Fermions with long range hopping. We thereby show that the distribution function of couplings $J$ at renormalization scale $Ω$ flows to the strong disorder fixed point distribution with small corrections at $\tilde{r} > ρ,$ which depend on power exponent $α$ and coupling anisotropy $γ.$ As a consequence, the low temperature magnetic susceptibility diverges with an anomalous power law. The distribution of singlet lengths $l$ is found to decay as $l^{-2}$. The entanglement entropy of a subsystem of length $n$ increases in the ground state logarithmically for all $α$ and $γ$. After a global quantum quench the entanglement entropy increases with time logarithmically as $S(t) \sim \ln(t)/(2α)$.

cond-mat.dis-nn↗

arXiv2024

SNS Junctions along the BCS-BEC Crossover

We present a theory of SNS junctions, a normal metal sandwiched between two superconductors, along the crossover from the BCS to the BEC regime. We calculate the Josephson current as a function of the chemical potential relative to the band edge in the superconducting region, $μ_S$, where the BEC phase is indicated by $μ_S <0$. The chemical potential relative to the band edge in the normal metal, $μ_N$, allows us to tune the junction between the SNS case ($μ_N>0$) and the SIS case, where the superconductors are separated by a tunneling barrier. We find that there are Andreev levels in the BEC regime, as long as there is sufficient density of states in the normal region, i.e. when $μ_N>Δ$, where $Δ$ is the amplitude of the superconducting order parameter. For 1D SNS junctions, we find the Josephson current $I_S$ carried by these Andreev levels to be a function of the ratio $Δ/Δ_d$, where $Δ_d$ is the Andreev level spacing. At zero temperature, the Josephson current has a maximum on the BCS side of the transition where $Δ$ is maximal. At finite temperature, however, we find that the maximum moves to the BEC side of the crossover. We identify the mechanism for this phenomenon to be the decrease in the number of Andreev levels at the BCS-BEC crossover, accompanied by an increase in excitation energy to the unoccupied levels, making it less likely that these states are thermally occupied. Thereby, at finite temperature, the Josephson current is more strongly reduced on the BCS side of the crossover, resulting in a maximal Josephson current at the BCS-BEC crossover.

cond-mat.supr-con↗

arXiv2024

Competition between Kondo Effect and RKKY Coupling

When magnetic moments are immersed into the Fermi sea of itinerant electrons, rich quantum physics emerges. This is relevant for a wide range of materials including heavy Fermion systems, high temperature superconductors like the cuprates, but also good metals with magnetic impurities, doped semiconductors like Si:P close to the metal-insulator transition, 2D materials like graphene and topological insulators. While each material has its specific properties, requiring detailed modelling, their electronic properties are to some degree governed by the competition between Kondo screening and indirect exchange couplings. In these lecture notes we give an introduction, starting with a review of formation of magnetic moments, the theory of the Kondo effect for a single magnetic impurity in a metal host and the derivation of RKKY coupling between magnetic impurities in a metal host. We review the Doniach diagram and Kondo lattice physics and give an introduction to a self consistent renormalization group theory, taking into account Kondo effect and RKKY coupling between magnetic impurities and review results obtained thereby. We review the effect of gaps and pseudo gaps on Kondo effect and RKKY couplings, and on their competition. Especially for dilute concentration of magnetic moments, disorder effects from randomly distributed impurities result in a distribution of both Kondo temperatures and RKKY couplings. Then, their competition becomes an even more complex problem. Moreover, disorder induced Anderson localization transitions may occur, affecting both Kondo effect and RKKY coupling severely, and changing their competition. These disorder effects on the spin competition are introduced and recent results are reviewed. We conclude with an outlook and list of, in our view, most pressing and interesting open problems.

cond-mat.str-el↗

arXiv2023

Local versus global stability in dynamical systems with consecutive Hopf-Bifurcations

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the concepts of local (linear) and global stability. Here, we show how systems displaying Hopf bifurcations show contrarian results on these two aspects of stability: Global stability is large close to the point where the system loses its local stability altogether. We demonstrate this effect for an elementary model system, an anharmonic oscillator and a realistic model of power system dynamics with delayed control. Detailed investigations of the bifurcation explain the seeming paradox in terms of the location of the attractors relative to the equilibrium.

nlin.AO↗

arXiv2023

Entanglement Entropy Growth in Disordered Spin Chains with Tunable Range Interactions

The non-equilibrium dynamics of disordered many-body quantum systems after a global quantum quench unveils important insights about the competition between interactions and disorder, yielding in particular an insightful perspective on many body localization (MBL). Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on the quantum quench dynamics have so far not been investigated. In this letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power $α$. Using a dynamical version of the strong disorder renormalization group (SDRG) we find for $α>α_c$ that the entanglement entropy grows logarithmically with time and becomes smaller with larger $α$ as $S(t) = S_p \ln(t)/(2α)$. Here, $S_p= 2 \ln2 -1$. We use numerical exact diagonalization (ED) simulations to verify our results for system sizes up to $ N\sim 16$ spins, yielding good agreement for sufficiently large $α> α_c \approx 1.8$. For $α<α_c$, we find that the entanglement entropy grows as a power-law with time, $S(t)\sim t^{γ(α)}$ with $0<γ(α)<1$ a decaying function of the interaction exponent $α$.

cond-mat.dis-nn↗

arXiv2022

Real-space BCS-BEC crossover in FeSe monolayer

The quantum many body states in the BCS-BEC crossover regime are of long-lasting interest. Here we report direct spectroscopic evidence of BCS-BEC crossover in real-space in a FeSe monolayer thin film by using spatially resolved scanning tunneling spectra. The crossover is driven by the shift of band structure relative to the Fermi level. The theoretical calculation based on a two-band model qualitatively reproduces the measured spectra in the whole crossover range. In addition, the Zeeman splitting of the quasi-particle states is found to be consistent with the characteristics of a condensate. Our work paves the way to study the exotic states of BCS-BEC crossover in a two-dimensional crystalline material at the atomic scale.

cond-mat.supr-con↗

arXiv2022

Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe

We consider the orthogonality catastrophe in the (extended) Aubry-André (AA)-Model, by calculating the overlap $F$ between the ground state of the Fermi liquid in that quasi-crystalline model and the one of the same system with an added potential impurity, as function of the size of that impurity. Recently, the typical fidelity $F_{\rm typ}$ was found in quantum critical phases to decay exponentially with system size $L$ as $F \sim \exp(-c L^{z η})$\cite{Kettemann2016} as found in an analytical derivation due to critical correlations. For the critical AA model $η= 1/2$ is the power of multifractal intensity correlations, and $z$ the dynamical exponent due to the fractal structure of the density of states which is numerically found to be $z \gg 1$. Surprisingly, however, we find for a weak single site impurity that the fidelity decays with a power law, in the critical phase. Even though it is found to be smaller and decays faster than in the metallic phase, it does not decay exponentially as predicted. We find an exponential AOC however in the insulator phase for which we give a statistical explanation, a mechanism which is profoundly different from the AOC in metals, where it is the coupling to a continuum of states which yields there the power law suppression of the fidelity. By reexamination of the analytical derivation we identify nonperturbative corrections due to the impurity potential and multipoint correlations among wave functions as possible causes for the absence of the exponential AOC in the critical phase. For an extended impurity, however, we find indications of an exponential AOC at the quantum critical point of the AA model and at the mobility edge of the extended AA model and suggest an explanation for this finding.

cond-mat.dis-nn↗

arXiv2022

Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions

Quantum information theoretical measures are useful tools for characterizing quantum dynamical phases. However, employing them to study excited states of random spin systems is a challenging problem. Here, we report results for the entanglement entropy (EE) scaling of excited eigenstates of random XX antiferromagnetic spin chains with long-range (LR) interactions decaying as a power law with distance with exponent $α$. To this end, we extend the real-space renormalization group technique for excited states (RSRG-X) to solve this problem with LR interaction. For comparison, we perform numerical exact diagonalization (ED) calculations. From the distribution of energy level spacings, as obtained by ED for up to $N\sim 18$ spins, we find indications of a delocalization transition at $α_c \approx 1$ in the middle of the energy spectrum. With RSRG-X and ED, we show that for $α>α^*$ the entanglement entropy (EE) of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for $α<α^*$ EE displays an algebraic growth with the subsystem size $l$, $S_l\sim l^β$, with $0<β<1$. We find that $α^* \approx 1$ coincides with the delocalization transition $α_c$ in the middle of the many-body spectrum. An interpretation of these results based on the structure of the RG rules is proposed, which is due to {\it rainbow} proliferation for very long-range interactions $α\ll 1$. We also investigate the effective temperature dependence of the EE allowing us to study the half-chain entanglement entropy of eigenstates at different energy densities, where we find that the crossover in EE occurs at $α^* < 1$.

cond-mat.dis-nn↗

arXiv2020

Complete Solution of the Tight Binding Model on a Cayley Tree: Strongly Localised versus Extended States

The complete set of Eigenstates and Eigenvalues of the nearest neighbour tight binding model on a Cayley tree with branching number $b=2$ and $M$ branching generations with open boundary conditions is derived. We find that of the $N= 1 +3 (2^M-1)$ total states only $3 M +1$ states are extended throughout the Cayley tree. The remaining $N-(3 M+1)$ states are found to be strongly localised states with finite amplitudes on only a subset of sites. In particular, there are, for $M>1$, $3 \times 2^{M-2}$ surface states which are each antisymmetric combinations of only two sites on the surface of the Cayley tree and have energy eactly at $E=0$, the middle of the band. The ground state and the first two excited states of the Cayley tree are found to be extended states with amplitudes on all sites of the Cayley tree, for all $M$. We use the results on the complete set of Eigenstates and Eigenvalues to derive the total density of states and a local density of states.

cond-mat.mes-hall↗

arXiv2020

Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $α$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α> 1/2$. A numerical implementation of the SDRG method yields a power law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $α$, corresponding to a critical behavior with an effective central charge $c = {\rm ln} 2$, independent of $α$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $α$. For a wide range of distances $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-la-decaying interaction with $α=2$. Consistent with this observation, we find using ED that the concurrence shows power law decay, albeit with smaller power exponents than obtained by SDRG.

cond-mat.dis-nn↗

arXiv2020

Multifractality and the distribution of the Kondo temperature at the Anderson transition

Using numerical simulations, we investigate the distribution of Kondo temperatures at the Anderson transition. In agreement with previous work, we find that the distribution has a long tail at small Kondo temperatures. Recently, an approximation for the tail of the distribution was derived analytically. This approximation takes into account the multifractal distribution of the wavefunction amplitudes (in the parabolic approximation), and power law correlations between wave function intensities, at the Anderson transition. It was predicted that the distribution of Kondo temperatures has a power law tail with a universal exponent. Here, we attempt to check that this prediction holds in a numerical simulation of Anderson's model of localisation in three dimensions.

cond-mat.mes-hall↗

arXiv2019

Time delay effects in the control of synchronous electricity grids

The expansion of inverter-connected generation facilities (i.e. wind and photovoltaics) and the removal of conventional power plants is necessary to mitigate the impacts of climate change. Whereas conventional generation with large rotating generator masses provides stabilizing inertia, inverter-connected generation does not. Since the underlying power system and the control mechanisms that keep it close to a desired reference state, were not designed for such a low inertia system, this might make the system vulnerable to disturbances. In this paper, we will investigate whether the currently used control mechanisms are able to keep a low inertia system stable and how this is effected by the time delay between a frequency deviation and the onset of the control action. We integrate the control mechanisms used in continental Europe into a model of coupled oscillators which resembles the second order Kuramoto model. This model is then used to investigate how the interplay of changing inertia, network topology and delayed control effects the stability of the interconnected power system. To identify regions in parameter space that make stable grid operation possible, the linearized system is analyzed to create the system's stability chart. We show that lower and distributed inertia could have a beneficial effect on the stability of the desired synchronous state.

nlin.AO↗

arXiv2019

Propagation of wind-power-induced fluctuations in power grids

Renewable generators perturb the electric power grid with heavily non-Gaussian and time correlated fluctuations. While changes in generated power on timescales of minutes and hours are compensated by frequency control measures, we report subsecond distribution grid frequency measurements with local non-Gaussian fluctuations which depend on the magnitude of wind power generation in the grid. Motivated by such experimental findings, we simulate the sub-second grid frequency dynamics by perturbing the power grid, as modeled by a network of phase coupled nonlinear oscillators, with synthetically generated wind power feed-in time series. We derive a linear response theory and obtain analytical results for the variance of frequency increment distributions. We find that the variance of short-term fluctuations decays, for large inertia, exponentially with distance to the feed-in node, in agreement with numerical results both for a linear chain of nodes and the German transmission grid topology. In sharp contrast, the kurtosis of frequency increments is numerically found to decay only slowly, not exponentially, in both systems, indicating that the non-Gaussian shape of frequency fluctuations persists over long ranges.

physics.soc-ph↗

arXiv2018

Analysis of the Dynamics and Topology Dependencies of Small Perturbations in Electric Transmission Grids

Through an eigenanalysis of small perturbations, as typically done in small-signal stability studies, we intend to discover the underlying reasons that make those perturbations propagate in some way or another in the grid. To this end, we establish connections between the perturbations time-scale and topological metrics. Namely, the algebraic connectivity and the Fiedler vector of a generalized/weighted Laplacian matrix that depends on the stationary phase solutions of the system and is thereby inherently conditioned by the topology and the power distribution. Then, we aim to find out the isolated influence of topology on the perturbations when the network interacting agents have, in principle, opposite behaviors (i.e. producers and consumers). To do so, we study three networks: Small-world, Random, German grid. Furthermore, we tackle the effect of machine clustering on small perturbations and the influence of the network's average clustering coefficient on the intensity localization of the generalized Fiedler vector. Finally, we propose ways in which future (dynamic topology control) and existing (power system stabilizer) grid control strategies can adapt their response to comprehensively consider the topology and remote signals in the system.

physics.soc-ph↗

arXiv2018

Propagation of Disturbances in AC Electricity Grids

The energy transition towards high shares of renewable energy will affect the stability of electricity grids in many ways. Here, we aim to study its impact on propagation of disturbances by solving nonlinear swing equations describing coupled rotating masses of synchronous generators and motors on different grid topologies. We consider a tree, a square grid and as a real grid topology, the German transmission grid. We identify ranges of parameters with different transient dynamics: the disturbance decays exponentially in time, superimposed by oscillations with the fast decay rate of a single node, or with a smaller decay rate without oscillations. Most remarkably, as the grid inertia is lowered, nodes may become correlated, slowing down the propagation from ballistic to diffusive motion, decaying with a power law in time. Applying linear response theory, we show that tree grids have a spectral gap leading to exponential relaxation as protected by topology and independent on grid size. Meshed grids are found to have a spectral gap which decreases with increasing grid size, leading to slow power law relaxation and collective diffusive propagation of disturbances. We conclude by discussing consequences if no measures are undertaken to preserve the grid inertia in the energy transition.

physics.soc-ph↗

arXiv2016

Cascading Failures in AC Electricity Grids

Sudden failure of a single transmission element in a power grid can induce a domino effect of cascading failures, which can lead to the isolation of a large number of consumers or even to the failure of the entire grid. Here we present results of the simulation of cascading failures in power grids, using an alternating current (AC) model. We first apply this model to a regular square grid topology. For a random placement of consumers and generators on the grid, the probability to find more than a certain number of unsupplied consumers decays as a power law and obeys a scaling law with respect to system size. Varying the transmitted power threshold above which a transmission line fails does not seem to change the power law exponent $q \approx 1.6$. Furthermore, we study the influence of the placement of generators and consumers on the number of affected consumers and demonstrate that large clusters of generators and consumers are especially vulnerable to cascading failures. As a real-world topology we consider the German high-voltage transmission grid. Applying the dynamic AC model and considering a random placement of consumers, we find that the probability to disconnect more than a certain number of consumers depends strongly on the threshold. For large thresholds the decay is clearly exponential, while for small ones the decay is slow, indicating a power law decay.

nlin.AO↗