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Tobias Müller

Publications and source records attributed to Tobias Müller.

At least 55 records · Page 3Linked to original sources
arXiv2022

Resolution of intramolecular dipoles and push-back effect of individual molecules on a metal surface

Molecules consisting of a donor and an acceptor moiety can exhibit large intrinsic dipole moments. Upon deposition on a metal surface, the dipole may be effectively screened and the charge distribution altered due to hybridization with substrate electronic states. Here, we deposit Ethyl-Diaminodicyanoquinone molecules, which exhibit a large dipole moment in gas phase, on a Au(111) surface. Employing a combination of scanning tunneling microscopy and non-contact atomic force microscopy, we find that a significant dipole moment persists in the flat-lying molecules. Density-functional theory calculations reveal that the dipole moment is even increased on the metal substrate as compared to the gas phase. We also show that the local contact potential across the molecular islands is decreased by several tens of meV with respect to the bare metal. We explain this by the induced charge-density redistribution due to the adsorbed molecules, which confine the substrate's wavefunction at the interface. Our local measurements provide direct evidence of this so-called push-back or cushion effect at the scale of individual molecules.

cond-mat.mes-hall↗
arXiv2022

Better Integrators for Functional Renormalization Group Calculations

We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice $t-t'$ Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations.

cond-mat.str-el↗
arXiv2022

Benchmark Calculations of Multiloop Pseudofermion fRG

The pseudofermion functional renormalization group (pffRG) is a computational method for determining zero-temperature phase diagrams of frustrated quantum magnets. In a recent methodological advance, the commonly employed Katanin truncation of the flow equations was extended to include multiloop corrections, thereby capturing additional contributions from the three-particle vertex [ arXiv:2011.01268 , arXiv:2011.01269 ]. This development has also stimulated significant progress in the numerical implementation of pffRG, allowing one to track the evolution of pseudofermion vertices under the renormalization group flow with unprecedented accuracy. However, cutting-edge solvers differ in their integration algorithms, heuristics to discretize Matsubara frequency grids, and more. To lend confidence in the numerical robustness of state-of-the-art multiloop pffRG codes, we present and compare results produced with two independently developed and algorithmically distinct solvers for Heisenberg models on three-dimensional lattice geometries. Using the cubic lattice Heisenberg (anti)ferromagnet with nearest and next-nearest neighbor interactions as a generic benchmark model, we find the two codes to quantitatively agree, often up to several orders of magnitude in digital precision, both on the level of spin-spin correlation functions and renormalized fermionic vertices for varying loop orders. These benchmark calculations further substantiate the usage of multiloop pffRG solvers to tackle unconventional forms of quantum magnetism.

cond-mat.str-el↗
arXiv2021

Solving Large Steiner Tree Problems in Graphs for Cost-Efficient Fiber-To-The-Home Network Expansion

The expansion of Fiber-To-The-Home (FTTH) networks creates high costs due to expensive excavation procedures. Optimizing the planning process and minimizing the cost of the earth excavation work therefore lead to large savings. Mathematically, the FTTH network problem can be described as a minimum Steiner Tree problem. Even though the Steiner Tree problem has already been investigated intensively in the last decades, it might be further optimized with the help of new computing paradigms and emerging approaches. This work studies upcoming technologies, such as Quantum Annealing, Simulated Annealing and nature-inspired methods like Evolutionary Algorithms or slime-mold-based optimization. Additionally, we investigate partitioning and simplifying methods. Evaluated on several real-life problem instances, we could outperform a traditional, widely-used baseline (NetworkX Approximate Solver) on most of the domains. Prior partitioning of the initial graph and the presented slime-mold-based approach were especially valuable for a cost-efficient approximation. Quantum Annealing seems promising, but was limited by the number of available qubits.

cs.AI↗
arXiv2021

Towards Multi-Agent Reinforcement Learning using Quantum Boltzmann Machines

Reinforcement learning has driven impressive advances in machine learning. Simultaneously, quantum-enhanced machine learning algorithms using quantum annealing underlie heavy developments. Recently, a multi-agent reinforcement learning (MARL) architecture combining both paradigms has been proposed. This novel algorithm, which utilizes Quantum Boltzmann Machines (QBMs) for Q-value approximation has outperformed regular deep reinforcement learning in terms of time-steps needed to converge. However, this algorithm was restricted to single-agent and small 2x2 multi-agent grid domains. In this work, we propose an extension to the original concept in order to solve more challenging problems. Similar to classic DQNs, we add an experience replay buffer and use different networks for approximating the target and policy values. The experimental results show that learning becomes more stable and enables agents to find optimal policies in grid-domains with higher complexity. Additionally, we assess how parameter sharing influences the agents behavior in multi-agent domains. Quantum sampling proves to be a promising method for reinforcement learning tasks, but is currently limited by the QPU size and therefore by the size of the input and Boltzmann machine.

cs.AI↗
arXiv2021

Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice

We investigate the nature of the ground-state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice by complementary state-of-the-art numerical techniques, such as variational Monte Carlo (VMC) with versatile Gutzwiller-projected Jastrow wave functions, unconstrained multi-variable variational Monte Carlo (mVMC), and pseudo-fermion/Majorana functional renormalization group (PF/PM-FRG) methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence-bond-crystal (VBC) orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest-energy variational ground state, and it is obtained as an instability of the U(1) Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer-dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing orders.

cond-mat.str-el↗
arXiv2021

On the contractibility of random Vietoris-Rips complexes

We show that the Vietoris-Rips complex $\mathcal R(n,r)$ built over $n$ points sampled at random from a uniformly positive probability measure on a convex body $K\subseteq \mathbb R^d$ is a.a.s. contractible when $r \geq c \left(\frac{\ln n}{n}\right)^{1/d}$ for a certain constant that depends on $K$ and the probability measure used. This answers a question of Kahle [Discrete Comput. Geom. 45 (2011), 553-573]. We also extend the proof to show that if $K$ is a compact, smooth $d$-manifold with boundary - but not necessarily convex - then $\mathcal R(n,r)$ is a.a.s. homotopy equivalent to $K$ when $c_1 \left(\frac{\ln n}{n}\right)^{1/d} \leq r \leq c_2$ for constants $c_1=c_1(K), c_2=c_2(K)$. Our proofs expose a connection with the game of cops and robbers.

math.CO↗
arXiv2021

Developing emotion recognition for video conference software to support people with autism

We develop an emotion recognition software for the use with a video conference software for autistic individuals which are unable to recognize emotions properly. It can get an image out of the video stream, detect the emotion in it with the help of a neural network and display the prediction to the user. The network is trained on facial landmark features. The software is fully modular to support adaption to different video conference software, programming languages and implementations.

cs.CV↗
arXiv2020

Clustering in a hyperbolic model of complex networks

In this paper we consider the clustering coefficient and clustering function in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at most a certain hyperbolic distance from each other. It has been shown that this model has various properties associated with complex networks, e.g. power-law degree distribution, short distances and non-vanishing clustering coefficient. Here we show that the clustering coefficient tends in probability to a constant $γ$ that we give explicitly as a closed form expression in terms of $α, ν$ and certain special functions. This improves earlier work by Gugelmann et al., who proved that the clustering coefficient remains bounded away from zero with high probability, but left open the issue of convergence to a limiting constant. Similarly, we are able to show that $c(k)$, the average clustering coefficient over all vertices of degree exactly $k$, tends in probability to a limit $γ(k)$ which we give explicitly as a closed form expression in terms of $α, ν$ and certain special functions. We are able to extend this last result also to sequences $(k_n)_n$ where $k_n$ grows as a function of $n$. Our results show that $γ(k)$ scales differently, as $k$ grows, for different ranges of $α$. More precisely, there exists constants $c_{α,ν}$ depending on $α$ and $ν$, such that as $k \to \infty$, $γ(k) \sim c_{α,ν} \cdot k^{2 - 4α}$ if $\frac{1}{2} < α< \frac{3}{4}$, $γ(k) \sim c_{α,ν} \cdot \log(k) \cdot k^{-1} $ if $α=\frac{3}{4}$ and $γ(k) \sim c_{α,ν} \cdot k^{-1}$ when $α> \frac{3}{4}$. These results contradict a claim of Krioukov et al., which stated that the limiting values $γ(k)$ should always scale with $k^{-1}$ as we let $k$ grow.

math.PR↗
arXiv2020

Component Games on Random Graphs

In the $\left(1:b\right)$ component game played on a graph $G$, two players, Maker and Breaker, alternately claim~$1$ and~$b$ previously unclaimed edges of $G$, respectively. Maker's aim is to maximise the size of a largest connected component in her graph, while Breaker is trying to minimise it. We show that the outcome of the game on the binomial random graph is strongly correlated with the appearance of a nonempty $(b+2)$-core in the graph. For any integer $k$, the $k$-core of a graph is its largest subgraph of minimum degree at least $k$. Pittel, Spencer and Wormald showed in 1996 that for any $k\ge3$ there exists an explicitly defined constant $c_{k}$ such that $p=c_{k}/n$ is the threshold function for the appearance of the $k$-core in $G(n,p)$. More precisely, $G(n,c/n)$ has WHP a linear-size $k$-core when the constant $c>c_{k}$, and an empty $k$-core when $c c_{b+2}$, while Breaker can WHP prevent Maker from building larger than polylogarithmic-size components if $c<c_{b+2}$. For Breaker's strategy, we prove a theorem which may be of independent interest. The standard algorithm for computing the $k$-core of any graph is to repeatedly delete ("peel") all vertices of degree less than $k$, as long as such vertices remain. When $G(n,c/n)$ for $c<c_{k}$, it was shown by Jiang, Mitzenmacher and Thaler that $\log_{k-1}\log n+Θ(1)$ peeling iterations are WHP necessary and sufficient to obtain the (empty) $k$-core of~$G$. Our theorem states that already after a constant number of iterations, $G$ is WHP shattered into pieces of polylogarithmic size.

math.CO↗
arXiv2020

Limiting probabilities of first order properties of random sparse graphs and hypergraphs

Let $G_n$ be the binomial random graph $G(n,p=c/n)$ in the sparse regime, which as is well-known undergoes a phase transition at $c=1$. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence $ϕ$, the limiting probability that $G_n$ satisfies $ϕ$ as $n\to\infty$ exists, and moreover it is an analytic function of $c$. In this paper we consider the closure $\overline{L_c}$ in $[0,1]$ of the set $L_c$ of all limiting probabilities of first order sentences in $G_n$. We show that there exists a critical value $c_0 \approx0.93$ such that $\overline{L_c}= [0,1]$ when $c \ge c_0$, whereas $\overline{L_c}$ misses at least one subinterval when $c<c_0$. We extend these results to random $d$-uniform sparse hypergraphs, where the probability of a hyperedge is given by $p=c/n^{d-1}$.

math.CO↗
arXiv2019

Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians

We address the long-standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal-space susceptibility. We show that the physics of these materials is principally governed by long-range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin liquids featuring degenerate manifolds of wave-vectors of different dimensions: A Coulomb phase with three-dimensional degeneracy for LiInCr4O8 and LiGaCr4O8, a spiral spin liquid with two-dimensional degeneracy for CuInCr4Se8 and one-dimensional line degeneracies characteristic of the face-centered cubic antiferromagnet for LiInCr4S8, LiGaCr4S8 and CuInCr4S8. The surprisingly complex array of prototypical pyrochlore behaviors we discovered in chromium spinels may inspire studies of transition paths between different semi-classical spin liquids by doping or pressure.

cond-mat.str-el↗
arXiv2019

A Load Balancing Surveillance Algorithm For Multifunctional Radar Resource Management

For all multifunctional radar systems the allocation of resources plays an outstanding role. Many radars have low priority on surveillance tasks. In challenging situations this leads to neglecting of surveillance beams in directions where many other tasks are done. This document presents a technique that enables multifunctional radar systems to keep on scanning overloaded surveillance sectors under the condition that all sectors have a similar revisit time. Since radar resource management depends on the used system, two general configurations are considered in this paper. The focus lies on systems with a rotating antenna.

eess.SP↗
arXiv2019

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

We investigate the spin $S=1/2$ Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, Néel, stripe and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins ($S=1/2$) we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations while no new long-range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for $S=1$. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available data

cond-mat.str-el↗
arXiv2019

The diameter of KPKVB random graphs

We consider a model for complex networks that was recently proposed as a model for complex networks by Krioukov et al. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at most a certain hyperbolic distance from each other. It has been previously shown that this model has various properties associated with complex networks, including a power-law degree distribution and a strictly positive clustering coefficient. The model is specified using three parameters : the number of nodes $N$, which we think of as going to infinity, and $α, ν> 0$ which we think of as constant. Roughly speaking $α$ controls the power law exponent of the degree sequence and $ν$ the average degree. Earlier work of Kiwi and Mitsche has shown that when $α< 1$ (which corresponds to the exponent of the power law degree sequence being $< 3$) then the diameter of the largest component is a.a.s.~polylogarithmic in $N$. Friedrich and Krohmer have shown it is a.a.s.~$Ω(\log N)$ and they improved the exponent of the polynomial in $\log N$ in the upper bound. Here we show the maximum diameter over all components is a.a.s.~$O(\log N)$ thus giving a bound that is tight up to a multiplicative constant.

math.PR↗
arXiv2019

Hamilton cycles and perfect matchings in the KPKVB model

In this paper we consider the existence of Hamilton cycles and perfect matchings in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at most a certain hyperbolic distance from each other. It has been previously shown that this model has various properties associated with complex networks, including a power-law degree distribution, "short distances" and a strictly positive clustering coefficient. The model is specified using three parameters: the number of nodes $n$, which we think of as going to infinity, and $α, ν> 0$, which we think of as constant. Roughly speaking $α$ controls the power law exponent of the degree sequence and $ν$ the average degree. Here we show that for every $α< 1/2$ and $ν=ν(α)$ sufficiently small, the model does not contain a perfect matching with high probability, whereas for every $α< 1/2$ and $ν=ν(α)$ sufficiently large, the model contains a Hamilton cycle with high probability.

math.PR↗
arXiv2019

Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions

We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin $S$ in the presence of nearest-neighbor $J_{1}$ and second-nearest-neighbor $J_{2}$ exchange interactions. By employing the pseudofermion functional renormalization group method, we find, for $S=1/2$ and $S=1$, an extended quantum-spin-liquid phase centered around $J_{2}=0$, which is shown to be robust against the introduction of breathing anisotropy. The effects of temperature, quantum fluctuations, breathing anisotropies, and a $J_{2}$ coupling on the nature of the scattering profile, and the pinch points, in particular, are studied. For the magnetic phases of the $J_{1}$-$J_{2}$ model, quantum fluctuations are shown to renormalize phase boundaries compared to the classical model and to modify the ordering wave vectors of spiral magnetic states, while no new magnetic orders are stabilized.

cond-mat.str-el↗