arXiv subjects

Wolfgang von der Linden

Publications and source records attributed to Wolfgang von der Linden.

At least 19 recordsLinked to original sources

arXiv2026

Slice Monte Carlo Integration

Numerical integration involving expensive target functions is a common bottleneck in Bayesian inference and simulation. When a cheap surrogate is available, standard approaches such as reweighting or importance sampling often suffer from high variance and inefficient use of function evaluations. We introduce Slice Monte Carlo integration (S$\ell$MC), a method that leverages a Nested Sampling-like procedure on the surrogate to partition the space into informative strata, or slices, while generating samples in the parameter space drawn from the prior within each slice. This enables stratified Monte Carlo integration of the expensive target function over the surrogate-induced partition, yielding an efficient estimate of the target integral. The surrogate level sets therefore make the induced ordering of the parameter space the relevant information for S$\ell$MC, rather than the pointwise target-to-surrogate ratios governing importance-sampling efficiency. Another key advantage of S$\ell$MC is the decoupling of slice volume estimation from the evaluation of the target, allowing the refinement of the slice-volume estimates without additional target evaluations. We investigate the properties of S$\ell$MC, demonstrate how to efficiently generate posterior samples, and assess its robustness in controlled Gaussian benchmark families with continuously tunable surrogate-target mismatch.

stat.ME↗

arXiv2024

Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we design a simple prototypical convolutional neural network and show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions and improve upon results reached by neural density operator based on the restricted Boltzmann machine. Hereby we give up the explicit restriction to positive semi-definite density matrices. However, this is fulfilled again to good approximation by optimizing the parameters. The great advantage of this approach is that it opens up the possibility of exploring more complex network architectures that can be tailored to specific physical properties. We show how translation invariance can be enforced effortlessly and reach better results with fewer parameters. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model compared to exact values.

quant-ph↗

arXiv2023

Quantum Transport in Open Spin Chains using Neural-Network Quantum States

In this work we study the treatment of asymmetric open quantum systems with neural networks based on the restricted Boltzmann machine. In particular, we are interested in the non-equilibrium steady state current in the boundary-driven (anisotropic) Heisenberg spin chain. We address previously published difficulties in treating asymmetric dissipative systems with neural-network quantum states and Monte-Carlo sampling and present an optimization method and a sampling technique that can be used to obtain high-fidelity steady state approximations of such systems. We point out some inherent symmetries of the Lindblad operator under consideration and exploit them during sampling. We show that local observables are not always a good indicator of the quality of the approximation and finally present results for the spin current that are in agreement with known results of simple open Heisenberg chains.

quant-ph↗

arXiv2022

In-silico synthesis of lowest-pressure high-$T_\text{c}$ ternary superhydrides

We report the theoretical prediction of two high-performing hydride superconductors BaSiH$_8$ and SrSiH$_8$. They are thermodynamically stable above pressures of $130$ and $174\,\text{GPa}$, respectively, and metastable below that. Employing anharmonic phonon calculations, we determine the minimum pressures of dynamical stability to be around $3\,\text{GPa}$ for BaSiH$_8$ and $27\,\text{GPa}$ for SrSiH$_8$, and using the fully anisotropic Migdal-Eliashberg theory, we predict $T_\text{c}$'s around $71$ and $126\,\text{K}$, respectively. We also introduce a method to estimate the lowest pressure of synthesis, based on the calculation of the enthalpy barriers protecting the BaSiH$_8$ $Fm\bar{3}m$ structure from decomposition at various pressures. This $kinetic$ pressure threshold is sensibly higher than the one based on $dynamic$ stability, but gives a much more rigorous limit for synthesizability.

cond-mat.supr-con↗

arXiv2022

Mapping Superconductivity in High-Pressure Hydrides: The $Superhydra$ Project

The discovery of high-$T_c$ conventional superconductivity in high-pressure hydrides has helped establish computational methods as a formidable tool to guide material discoveries in a field traditionally dominated by serendipitous experimental search. This paves the way to an ever-increasing use of data-driven approaches to the study and design of superconductors. In this work, we propose a new method to generate meaningful datasets of superconductors, based on element substitution into a small set of representative structural templates, generated by crystal structure prediction methods (MultiTemplate-HighThroughput approach). Our approach realizes an optimal compromise between structural variety and computational efficiency, and can be easily generalized to other elements and compositions. As a first application, we apply it to binary hydrides at high pressure, realizing a database of 880 hypothetical structures, characterized with a set of electronic, vibrational and chemical descriptors. 139 structures of our $Superhydra$ Database are superconducting according to the McMillan-Allen-Dynes approximation. Studying the distribution of $T_c$ and other properties across the database with advanced statistical and visualization techniques, we are able to obtain comprehensive material maps of the phase space of binary hydrides. The $Superhydra$ database can be thought as a first step of a generalized effort to map conventional superconductivity.

cond-mat.supr-con↗

arXiv2022

Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate

Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been shown that even the healthy aortic wall has an inherent heterogeneous microstructure. Some parts of the aorta are particularly susceptible to the development of inhomogeneities due to pathological changes, however, the distribution in the aortic wall and the spatial extent, such as size, shape, and type, are difficult to predict. Motivated by this observation, we describe the heterogeneous distribution of elastic fiber degradation in the dissected aortic wall using a stochastic constitutive model. For this purpose, random field realizations, which model the stochastic distribution of degraded elastic fibers, are generated over a non-equidistant grid. The random field then serves as input for a uni-axial extension test of the pathological aortic wall, solved with the finite-element (FE) method. To include the microstructure of the dissected aortic wall, a constitutive model developed in a previous study is applied, which also includes an approach to model the degradation of inter-lamellar elastic fibers. Then to assess the uncertainty in the output stress distribution due to this stochastic constitutive model, a convolutional neural network, specifically a Bayesian encoder-decoder, was used as a surrogate model that maps the random input fields to the output stress distribution obtained from the FE analysis. The results show that the neural network is able to predict the stress distribution of the FE analysis while significantly reducing the computational time. In addition, it provides the probability for exceeding critical stresses within the aortic wall, which could allow for the prediction of delamination or fatal rupture.

stat.ML↗

arXiv2021

Bayesian Surrogate Analysis and Uncertainty Propagation

The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model's credibility. For computationally expensive simulations, this is often feasible only via surrogate models that are learned from a small set of simulation samples. The surrogate models are commonly chosen and deemed trustworthy based on heuristic measures, and substituted for the simulation in order to approximately propagate the simulation input uncertainties to the simulation output. In the process, the contribution of the uncertainties of the surrogate itself to the simulation output uncertainties are usually neglected. In this work, we specifically address the case of doubtful surrogate trustworthiness, i.e. non-negligible surrogate uncertainties. We find that Bayesian probability theory yields a natural measure of surrogate trustworthiness, and that surrogate uncertainties can easily be included in simulation output uncertainties. For a Gaussian likelihood for the simulation data, with unknown surrogate variance and given a generalized linear surrogate model, the resulting formulas reduce to simple matrix multiplications. The framework contains Polynomial Chaos Expansions as a special case, and is easily extended to Gaussian Process Regression. Additionally, we show a simple way to implicitly include spatio-temporal correlations. Lastly, we demonstrate a numerical example where surrogate uncertainties are in part negligible and in part non-negligible.

stat.ME↗

arXiv2021

La-$X$-H hydrides: is hot superconductivity possible?

Motivated by the recent claim of hot superconductivity with critical temperatures up to 550 K in La + x hydrides (arXiv:2006.03004), we investigate the high-pressure phase diagram of possible compounds that may have formed in the experiment, using first-principles calculations for evolutionary crystal structure prediction and superconductivity. Starting from the hypothesis that the observed T$_c$ may be realized by successive heating upon a pre-formed LaH$_{10}$ phase, we examine plausible ternaries of lanthanum, hydrogen and other elements present in the diamond anvil cell: boron, nitrogen, carbon, platinum, gallium, gold. We find that only boron forms superhydride-like structures that can host high-Tc superconductivity, but the predicted Tc are incompatibe with the experimental reports. Our results indicate that, while the claims of hot superconductivity should be reconsidered, it is very likely that unkwown H-rich ternary or multinary phases containing lanthanum, boron and hydrogen may have formed under the reported experimental conditions, and that these may exhibit superconducting properties comparable, or even superior, to those of currently known hydrides.

cond-mat.supr-con↗

arXiv2021

LaBH$_{8}$: the first high-T$_{c}$ low-pressure superhydride

In the last five years a large number of new high-temperature superconductors have been predicted and experimentally discovered among hydrogen-rich crystals, at pressures which are way too high to meet any practical application. In this work, we report the computational prediction of a hydride superconductor, LaBH$_{8}$, with a T$_{c}$ of 126 K at a pressure of 50 GPa, thermodynamically stable above 100 GPa, and dynamically stable down to 40 GPa, an unprecedentedly low pressure for high-T$_{c}$ hydrides. LaBH$_{8}$ can be seen as a ternary sodalite-like hydride, in which a metallic hydrogen sublattice is stabilized by the chemical pressure exerted by the guest elements. The combination of two elements with different atomic sizes in LaBH$_{8}$ realizes a more efficient packing of atoms than in binary sodalite hydrides. A suitable choice of elements may be exploited to further reduce the stabilization pressure to ambient conditions.

cond-mat.supr-con↗

arXiv2021

Importance of feature engineering and database selection in a machine learning model: A case study on carbon crystal structures

Drive towards improved performance of machine learning models has led to the creation of complex features representing a database of condensed matter systems. The complex features, however, do not offer an intuitive explanation on which physical attributes do improve the performance. The effect of the database on the performance of the trained model is often neglected. In this work we seek to understand in depth the effect that the choice of features and the properties of the database have on a machine learning application. In our experiments, we consider the complex phase space of carbon as a test case, for which we use a set of simple, human understandable and cheaply computable features for the aim of predicting the total energy of the crystal structure. Our study shows that (i) the performance of the machine learning model varies depending on the set of features and the database, (ii) is not transferable to every structure in the phase space and (iii) depends on how well structures are represented in the database.

cond-mat.mtrl-sci↗

arXiv2021

Fused borophenes: a new family of superhard materials

The search of new superhard materials has received a strong impulse by industrial demands for low-cost alternatives to diamond and $c$-BN, such as metal borides. In this Letter we introduce a new family of superhard materials, "fused borophenes", containing 2D boron layers which are interlinked to form a 3D network. These materials, identified through a high-throughput scan of BxC1-x structures, exhibit Vicker's hardnesses comparable to those of the best commercial metal borides. Due to their low formation enthalpies, fused borophenes could be synthesized by high-temperature methods, starting from appropriate precursors, or through quenching of high-pressure phases.

cond-mat.mtrl-sci↗

arXiv2020

Efficient energy resolved quantum master equation for transport calculations in large strongly correlated systems

We introduce a systematic approximation for an efficient evaluation of Born--Markov master equations for steady state transport studies in open quantum systems out of equilibrium: the energy resolved master equation approach. The master equation is formulated in the eigenbasis of the open quantum system and build successively by including eigenstates with increasing grandcanonical energies. In order to quantify convergence of the approximate scheme we introduce quality factors to check preservation of trace, positivity and hermiticity. Furthermore, we discuss different types of master equations that go beyond the commonly used secular approximation in order to resolve coherences between quasi--degenerate states. For the discussion of complete positivity we introduce a canonical Redfield-Bloch master equation and compare it to a previously derived master equations in Lindblad form with and without using the secular approximation. The approximate scheme is benchmarked for a six orbital quantum system which shows destructive quantum interference under the application of a bias voltage. The energy resolved master equation approach presented here makes quantum transport calculations in many--body quantum systems numerically accessible also beyond six orbitals with a full Hilbert space of the order of $\sim 10^6$.

quant-ph↗

arXiv2020

Comment on "Pentadiamond: A Hard Carbon Allotrope of a Pentagonal Network of sp2 and sp3 C Atoms"

In a recent Letter, Fujii et. al. [Phys. Rev. Lett. 125, 016001] predicted a new carbon allotrope, pentadiamond, with remarkable mechanical properties: elastic moduli comparable or larger than diamond, and negative Poisson's ratio $μ$ = -0.241. The estimated Vicker's hardness is 422 GPa, $\sim$4.6 times higher than in diamond($\sim$92 GPa), the hardest material known to date. Pentadiamond, however was not investigated. Motivated by this, we used different approaches to estimate the elastic properties of pentadiamond with different approximations based on Density Functional Theory. The tests were also carried out on diamond and other known hard carbon allotropes for validation. Through tests, we found that the elastic constants and elastic moduli of pentadiamond reported in Ref. [Phys. Rev. Lett. 125, 016001] are incorrect, and pentadiamond should be considered a non-auxetic soft carbon allotrope.

cond-mat.mtrl-sci↗

arXiv2020

Phase Diagram and Superconductivity of Calcium Borohyrides at Extreme Pressures

Motivated by the recent discovery of near-room temperature superconductivity in high-pressure superhydrides, we investigate from first-principles the high-pressure superconducting phase diagram of the ternary Ca-B-H system, using ab-initio evolutionary crystal structure prediction, and Density Functional Perturbation Theory. We find that below 100 GPa all stable and weakly metastable phases are insulating. This pressure marks the appearance of several new chemically-forbidden phases on the hull of stability, and the first onset of metalization in CaBH$_5$. Metallization is then gradually achieved at higher pressure at different compositions. Among the metallic phases stable in the Megabar regime, we predict two high-$T_c$ superconducting phases with CaBH$_6$ and Ca$_2$B$_2$H$_{13}$ compositions, with critical temperatures of 119 and 89 K at 300 GPa, respectively, surviving to lower pressures. Ternary hydrides will most likely play a major role in superconductivity research in the coming years; our study suggests that, in order to reduce the pressure for the onset of metallicity and superconductivity, further explorations of ternary hydrides should focus on elements less electronegative than boron.

cond-mat.supr-con↗

arXiv2020

High-Temperature Conventional Superconductivity in the Boron-Carbon system: Material Trends

In this work we probe the possibility of high-temperature conventional superconductivity in the boron-carbon system, using ab-initio screening. A database of 320 metastable structures with fixed composition (50$\%$/50$\%$) is generated with the Minima-Hopping method, and characterized with electronic and vibrational descriptors. Full electron-phonon calculations on sixteen representative structures allow to identify general trends in $T_{\textrm{c}}$ across and within the four families in the energy landscape, and to construct an approximate $T_{\textrm{c}}$ predictor, based on transparently interpretable and easily computable electronic and vibrational descriptors. Based on these, we estimate that around 10$\%$ of all metallic structures should exhibit $T_{\textrm{c}}$'s above 30 $K$. This work is a first step towards ab-initio design of new high-$T_{\textrm{c}}$ superconductors.

cond-mat.supr-con↗

arXiv2019

Bayesian parametric analytic continuation of Green's functions

Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Green's function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the spectral function is inferred from a suitable set of parametrized basis functions. Bayesian model comparison then allows to assess the reliability of different parametrizations. The required evidence integrals of such a model comparison are determined by nested sampling. Compared to the maximum entropy method (MEM), routinely used for the analytic continuation of CTQMC data, the presented approach allows to infer whether the data support specific structures of the spectral function. We demonstrate the capability of BPAC in terms of CTQMC data for an Anderson impurity model (AIM) that shows a generalized Kondo scenario and compare the BPAC reconstruction to the MEM as well as to the spectral function obtained from the real-time fork tensor product state impurity solver where no analytic continuation is required. Furthermore, we present a combination of MEM and BPAC and its application to an AIM arising from the ab initio treatment of SrVO$_3$.

cond-mat.str-el↗

arXiv2019

First-principles quantum transport simulation of CuPc on Au(111) and Ag(111)

We investigate equilibrium and transport properties of a copper phthalocyanine (CuPc) molecule adsorbed on Au(111) and Ag(111) surfaces. The CuPc molecule has essentially three localized orbitals close to the Fermi energy resulting in strong local Coulomb repulsion not accounted for properly in density functional calculations. Hence, they require a proper many-body treatment within, e.g., the Anderson impurity model (AIM). The occupancy of these orbitals varies with the substrate on which CuPc is adsorbed. Starting from density functional theory calculations, we determine the parameters for the AIM embedded in a noninteracting environment that describes the residual orbitals of the entire system. While correlation effects in CuPc on Au(111) are already properly described by a single orbital AIM, for CuPc on Ag(111) the three orbital AIM problem can be simplified into a two orbital problem coupled to the localized spin of the third orbital. This results in a Kondo effect with a mixed character, displaying a symmetry between SU(2) and SU(4). The computed Kondo temperature is in good agreement with experimental values. To solve the impurity problem we use the recently developed fork tensor product state solver. To obtain transport properties, a scanning tunneling microscope (STM) tip is added to the CuPc molecule absorbed on the surface. We find that the transmission depends on the detailed position of the STM tip above the CuPc molecule in good agreement with differential conductance measurements.

cond-mat.str-el↗

arXiv2019

Non-equilibrium Green's functions and their relation to the negative differential conductance in the interacting resonant level model

We evaluate the non-equilibrium single particle Green's functions in the steady state of the interacting resonant level model (IRLM) under the effect of an applied bias voltage. Employing the so-called auxiliary master equation approach, we present accurate nonperturbative results for the non-equilibrium spectral and effective distribution functions, as well as for the current-voltage characteristics. We find a drastic change of these spectral properties between the regimes of low and high bias voltages and discuss the relation of these changes to the negative differential conductance (NDC), a prominent feature in the non-equilibrium IRLM. The anomalous evolution of the distribution function next to the impurity shown by our calculations suggests a mechanism whereby the impurity gets effectively decoupled from the leads at voltages where the NDC sets in, in agreement with previous renormalization group approaches. This scenario is qualitatively confirmed by a Hartree-Fock treatment of the model.

cond-mat.str-el↗