arXiv subjects

Tobias Müller

Publications and source records attributed to Tobias Müller.

At least 37 records · Page 2Linked to original sources

arXiv2024

Pseudo-fermion functional renormalization group for spin models

For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow of $m$-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.

cond-mat.str-el↗

arXiv2024

Measurement Uncertainty: Relating the uncertainties of physical and virtual measurements

In the context of industrially mass-manufactured products, quality management is based on physically inspecting a small sample from a large batch and reasoning about the batch's quality conformance. When complementing physical inspections with predictions from machine learning models, it is crucial that the uncertainty of the prediction is known. Otherwise, the application of established quality management concepts is not legitimate. Deterministic (machine learning) models lack quantification of their predictive uncertainty and are therefore unsuitable. Probabilistic (machine learning) models provide a predictive uncertainty along with the prediction. However, a concise relationship is missing between the measurement uncertainty of physical inspections and the predictive uncertainty of probabilistic models in their application in quality management. Here, we show how the predictive uncertainty of probabilistic (machine learning) models is related to the measurement uncertainty of physical inspections. This enables the use of probabilistic models for virtual inspections and integrates them into existing quality management concepts. Thus, we can provide a virtual measurement for any quality characteristic based on the process data and achieve a 100 percent inspection rate. In the field of Predictive Quality, the virtual measurement is of great interest. Based on our results, physical inspections with a low sampling rate can be accompanied by virtual measurements that allow an inspection rate of 100 percent. We add substantial value, especially to complex process chains, as faulty products/parts are identified promptly and upcoming process steps can be aborted.

stat.AP↗

arXiv2024

Phase diagram of the $J$-$J_d$ Heisenberg Model on the Maple-Leaf Lattice: Neural networks and density matrix renormalization group

We microscopically analyze the nearest neighbor Heisenberg model on the maple-leaf lattice through neural quantum states (NQS) and infinite density matrix renormalization group (iDMRG). Embarking to parameter regimes beyond the exact dimer singlet ground state with a dimer bond spin exchange coupling $J_d$ varied against the exchange strength $J$ of all other bonds, iDMRG (NQS) finds a dimer state paramagnetic phase for $J_d/J > 1.464$ ($J_d/J > 1.39$) and a canted $120^\circ$ magnetic order for $J_d/J < 1.419$ ($J_d/J < 1.23$). Assessing training convergence inaccuracies of NQS and the influence of finite cylindric circumference for iDMRG, we discuss the possible existence of an intermediate phase between magnet and dimer paramagnet.

cond-mat.str-el↗

arXiv2023

$\require{mhchem}$Quantum paramagnetism in the decorated square-kagome antiferromagnet $\ce{Na6Cu7BiO4(PO4)4Cl3}$

$\require{mhchem}$The square-kagome lattice Heisenberg antiferromagnet is a highly frustrated Hamiltonian whose material realizations have been scarce. We theoretically investigate the recently synthesized $\ce{Na6Cu7BiO4(PO4)4Cl3}$ where a Cu$^{2+}$ spin-$1/2$ square-kagome lattice (with six site unit cell) is decorated by a seventh magnetic site alternatingly above and below the layers. The material does not show any sign of long-range magnetic order down to 50 mK despite a Curie-Weiss temperature of $-212$ K indicating a quantum paramagnetic phase. Our DFT energy mapping elicits a purely antiferromagnetic Hamiltonian that features longer range exchange interactions beyond the pure square-kagome model and, importantly, we find the seventh site to be strongly coupled to the plane. We combine two variational Monte Carlo approaches, pseudo-fermion/Majorana functional renormalization group and Schwinger-Boson mean field calculations to show that the complex Hamiltonian of $\ce{Na6Cu7BiO4(PO4)4Cl3}$ still features a nonmagnetic ground state. We explain how the seventh Cu$^{2+}$ site actually aids the stabilization of the disordered state. We predict static and dynamic spin structure factors to guide future neutron scattering experiments.

cond-mat.str-el↗

arXiv2023

Maple Leaf Antiferromagnet in a Magnetic Field

We analyze the quantum antiferromagnet on the maple leaf lattice in the presence of a magnetic field. Starting from its exact dimer ground state and for a magnetic field strength of the order of the local dimer spin exchange coupling, we perform a strong coupling expansion and extract an effective hardcore boson model. The interplay of effective many-body interactions, suppressed single-particle dynamics, and correlated hopping gives way to an intriguing series of superfluid to insulator transitions which correspond to magnetization plateaux in terms of the maple leaf spin degrees of freedom. While we find plateaux at intermediate magnetization to be dominated by bosonic density wave order, we conjecture plateau formation from multi-boson bound states due to correlated hopping for lower magnetization.

cond-mat.str-el↗

arXiv2023

SoK: Assessing the State of Applied Federated Machine Learning

Machine Learning (ML) has shown significant potential in various applications; however, its adoption in privacy-critical domains has been limited due to concerns about data privacy. A promising solution to this issue is Federated Machine Learning (FedML), a model-to-data approach that prioritizes data privacy. By enabling ML algorithms to be applied directly to distributed data sources without sharing raw data, FedML offers enhanced privacy protections, making it suitable for privacy-critical environments. Despite its theoretical benefits, FedML has not seen widespread practical implementation. This study aims to explore the current state of applied FedML and identify the challenges hindering its practical adoption. Through a comprehensive systematic literature review, we assess 74 relevant papers to analyze the real-world applicability of FedML. Our analysis focuses on the characteristics and emerging trends of FedML implementations, as well as the motivational drivers and application domains. We also discuss the encountered challenges in integrating FedML into real-life settings. By shedding light on the existing landscape and potential obstacles, this research contributes to the further development and implementation of FedML in privacy-critical scenarios.

cs.LG↗

arXiv2023

Quality of Service Based Radar Resource Management for Navigation and Positioning

In hostile environments, GNSS is a potentially unreliable solution for self-localization and navigation. Many systems only use an IMU as a backup system, resulting in integration errors which can dramatically increase during mission execution. We suggest using a fighter radar to illuminate satellites with known trajectories to enhance the self-localization information. This technique is time-consuming and resource-demanding but necessary as other tasks depend on the self-localization accuracy. Therefore an adaption of classical resource management frameworks is required. We propose a quality of service based resource manager with capabilities to account for inter-task dependencies to optimize the self-localization update strategy. Our results show that this leads to adaptive navigation update strategies, mastering the trade-off between self-localization and the requirements of other tasks.

eess.SP↗

arXiv2023

Unlocking the Potential of Collaborative AI -- On the Socio-technical Challenges of Federated Machine Learning

The disruptive potential of AI systems roots in the emergence of big data. Yet, a significant portion is scattered and locked in data silos, leaving its potential untapped. Federated Machine Learning is a novel AI paradigm enabling the creation of AI models from decentralized, potentially siloed data. Hence, Federated Machine Learning could technically open data silos and therefore unlock economic potential. However, this requires collaboration between multiple parties owning data silos. Setting up collaborative business models is complex and often a reason for failure. Current literature lacks guidelines on which aspects must be considered to successfully realize collaborative AI projects. This research investigates the challenges of prevailing collaborative business models and distinct aspects of Federated Machine Learning. Through a systematic literature review, focus group, and expert interviews, we provide a systemized collection of socio-technical challenges and an extended Business Model Canvas for the initial viability assessment of collaborative AI projects.

cs.AI↗

arXiv2023

SEQUENT: Towards Traceable Quantum Machine Learning using Sequential Quantum Enhanced Training

Applying new computing paradigms like quantum computing to the field of machine learning has recently gained attention. However, as high-dimensional real-world applications are not yet feasible to be solved using purely quantum hardware, hybrid methods using both classical and quantum machine learning paradigms have been proposed. For instance, transfer learning methods have been shown to be successfully applicable to hybrid image classification tasks. Nevertheless, beneficial circuit architectures still need to be explored. Therefore, tracing the impact of the chosen circuit architecture and parameterization is crucial for the development of beneficially applicable hybrid methods. However, current methods include processes where both parts are trained concurrently, therefore not allowing for a strict separability of classical and quantum impact. Thus, those architectures might produce models that yield a superior prediction accuracy whilst employing the least possible quantum impact. To tackle this issue, we propose Sequential Quantum Enhanced Training (SEQUENT) an improved architecture and training process for the traceable application of quantum computing methods to hybrid machine learning. Furthermore, we provide formal evidence for the disadvantage of current methods and preliminary experimental results as a proof-of-concept for the applicability of SEQUENT.

quant-ph↗

arXiv2023

Nature of unconventional pairing in the kagome superconductors AV$_3$Sb$_5$

The recent discovery of AV$_3$Sb$_5$ (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple with multiple van Hove singularities close to the Fermi level for AV$_3$Sb$_5$, we provide a random phase approximation analysis of superconducting instabilities. Non-local Coulomb repulsion, the sublattice profile of the van Hove bands, and the bare interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in AV$_3$Sb$_5$.

cond-mat.supr-con↗

arXiv2023

Quality of service based radar resource management for synchronisation problems

An intelligent radar resource management is an essential building block of any modern radar system. The quality of service based resource allocation model (Q-RAM) provides a framework for profound and quantifiable decision-making but lacks a representation of inter-task dependencies that can e.g. arise for tracking and synchronisation tasks. As a consequence, synchronisation is usually performed in fixed non-optimal patterns. We present an extension of Q-RAM which enables the resource allocation to consider complex inter-task dependencies and can produce adaptive and intelligent synchronisation schemes. The provided experimental results demonstrate a significant improvement over traditional strategies.

eess.SP↗

arXiv2023

Poisson-Voronoi percolation in the hyperbolic plane with small intensities

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster is asymptotically equal to $πλ/3$ as $λ\to0.$ This answers a question of Benjamini and Schramm.

math.PR↗

arXiv2023

Training one model to detect heart and lung sound events from single point auscultations

Objective: This work proposes a semi-supervised training approach for detecting lung and heart sounds simultaneously with only one trained model and in invariance to the auscultation point. Methods: We use open-access data from the 2016 Physionet/CinC Challenge, the 2022 George Moody Challenge, and from the lung sound database HF_V1. We first train specialist single-task models using foreground ground truth (GT) labels from different auscultation databases to identify background sound events in the respective lung and heart auscultation databases. The pseudo-labels generated in this way were combined with the ground truth labels in a new training iteration, such that a new model was subsequently trained to detect foreground and background signals. Benchmark tests ensured that the newly trained model could detect both, lung, and heart sound events in different auscultation sites without regressing on the original task. We also established hand-validated labels for the respective background signal in heart and lung sound auscultations to evaluate the models. Results: In this work, we report for the first time results for i) a multi-class prediction for lung sound events and ii) for simultaneous detection of heart and lung sound events and achieve competitive results using only one model. The combined multi-task model regressed slightly in heart sound detection and gained significantly in lung sound detection accuracy with an overall macro F1 score of 39.2% over six classes, representing a 6.7% improvement over the single-task baseline models. Conclusion/Significance: To the best of our knowledge, this is the first approach developed to date for measuring heart and lung sound events invariant to both, the auscultation site and capturing device. Hence, our model is capable of performing lung and heart sound detection from any auscultation location.

cs.SD↗

arXiv2023

Effective spin-1 breathing kagome Hamiltonian induced by the exchange hierarchy in the maple leaf mineral bluebellite

As a highly frustrated model Hamiltonian with an exact dimer ground state, the Heisenberg antiferromagnet on the maple leaf lattice is of high theoretical interest, and a material realization is intensely sought after. We determine the magnetic Hamiltonian of the copper mineral bluebellite using density functional theory based energy mapping. As a consequence of the significant distortion of the spin $S=1/2$ maple leaf lattice, we find two of the five distinct nearest neighbor couplings to be ferromagnetic. Solution of this Hamiltonian with density matrix renormalization group calculations points us to the surprising insight that this particular imperfect maple leaf lattice, due to the strongly ferromagnetic Cu$^{2+}$ dimer, realizes an effective $S=1$ breathing kagome Hamiltonian. In fact, this is another highly interesting Hamiltonian which has rarely been realized in materials. Analysis of the effective model within a bond-operator formalism allows us to identify a valence bond solid ground state and to extract thermodynamic quantities using a low-energy bosonic mean-field theory. We resolve the puzzle of the apparent one-dimensional character of bluebellite as our calculated specific heat has a Bonner-Fisher-like shape, in good agreement with experiment.

cond-mat.str-el↗

arXiv2022

Observation of cnoidal wave localization in non-linear topolectric circuits

We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of non-linearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a non-linear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the non-linear SSH circuit follows the Korteweg-de Vries equation. The topological SSH boundary state which relates to a midgap impedance peak in the linearized limit is distorted into the LCn state in the non-linear regime, where the cnoidal eccentricity decreases from edge to bulk.

cond-mat.mes-hall↗

arXiv2022

Another Exact Ground State of a 2D Quantum Antiferromagnet

We present the exact dimer ground state of a quantum antiferromagnet on the maple-leaf lattice. A coupling anisotropy for one of the three inequivalent nearest-neighbor bonds is sufficient to stabilize the dimer state. Together with the Shastry-Sutherland Hamiltonian, we show that this is the only other model with an exact dimer ground state for all two-dimensional lattices with uniform tilings.

cond-mat.str-el↗

arXiv2022

Cycles in Mallows random permutations

We study cycle counts in permutations of $1,\dots,n$ drawn at random according to the Mallows distribution. Under this distribution, each permutation $π\in S_n$ is selected with probability proportional to $q^{\text{inv}(π)}$, where $q>0$ is a parameter and $\text{inv}(π)$ denotes the number of inversions of $π$. For $\ell$ fixed, we study the vector $(C_1(Π_n),\dots,C_\ell(Π_n))$ where $C_i(π)$ denotes the number of cycles of length $i$ in $π$ and $Π_n$ is sampled according to the Mallows distribution. Here we show that if $0 1$ there is striking difference between the behaviour of the even and the odd cycles. The even cycle counts still have linear means, and when properly rescaled tend to a multivariate Gaussian distribution. For the odd cycle counts on the other hand, the limiting behaviour depends on the parity of $n$ when $q>1$. Both $(C_1(Π_{2n}),C_3(Π_{2n}),\dots)$ and $(C_1(Π_{2n+1}),C_3(Π_{2n+1}),\dots)$ have discrete limiting distributions -- they do not need to be renormalized -- but the two limiting distributions are distinct for all $q>1$. We describe these limiting distributions in terms of Gnedin and Olshanski's bi-infinite extension of the Mallows model. We also investigate these limiting distributions, and study the behaviour of the constants involved in the Gaussian limit laws. We for example show that as $q\downarrow 1$ the expected number of 1-cycles tends to $1/2$ -- which, curiously, differs from the value corresponding to $q=1$. In addition we exhibit an interesting "oscillating" behaviour in the limiting probability measures for $q>1$ and $n$ odd versus $n$ even.

math.PR↗

arXiv2022

Pinch-points to half-moons and up in the stars: the kagome skymap

Pinch point singularities, associated with flat band magnetic excitations, are tell-tale signatures of Coulomb spin liquids. While their properties in the presence of quantum fluctuations have been widely studied, the fate of the complementary non-analytic features -- shaped as half-moons and stars -- arising from adjacent shallow dispersive bands has remained unexplored. Here, we address this question for the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with second and third neighbor couplings, which allows one to tune the classical ground state from flat bands to being governed by shallow dispersive bands for intermediate coupling strengths. Employing the complementary strengths of variational Monte Carlo, pseudo-fermion functional renormalization group, and density-matrix renormalization group, we establish the quantum phase diagram. The U(1) Dirac spin liquid ground state of the nearest-neighbor antiferromagnet remains remarkably robust till intermediate coupling strengths when it transitions into a pinwheel valence bond crystal displaying signatures of half-moons in its structure factor. Our work thus identifies a microscopic setting that realizes one of the proximate orders of the Dirac spin liquid identified in a recent work [Song, Wang, Vishwanath, He, Nat. Commun. 10, 4254 (2019)]. For larger couplings, we obtain a collinear magnetically ordered ground state characterized by star-like patterns.

cond-mat.str-el↗