arXiv subjects

Johannes Hofmann

Publications and source records attributed to Johannes Hofmann.

At least 37 records · Page 2Linked to original sources

arXiv2023

Anomalously long lifetimes in two-dimensional Fermi liquids

A precise characterization of the recently discovered crossover to hydrodynamic transport in electron liquids, and in particular of a conjectured exotic odd-parity transport regime, requires a full solution of the Fermi-liquid collision integral at all temperatures beyond state-of-the-art analytic leading-logarithmic approximations. We develop a general basis expansion of the linearized collision integral applicable at all temperatures, and employ this to determine the decay rates of Fermi surface perturbations in two-dimensional electron liquids. In particular, we provide exhaustive data on the decay rates for a new odd-parity regime, in which parity-even Fermi surface deformations decay rapidly but odd-parity modes are anomalously long lived. We find that this transport regime exists at fairly large temperatures $T \lesssim 0.1 T_F$, putting this regime within the reach of current experiments.

cond-mat.mes-hall↗

arXiv2023

Scale Invariance in the Lowest Landau Level

We show that the discrete set of pair amplitudes $A_m$ introduced by Haldane are an angular-momentum resolved generalization of the Tan two-body contact, which parametrizes universal short-range correlations in atomic quantum gases. The pair amplitudes provide a complete description of translation-invariant and rotation-invariant states in the lowest Landau level (LLL), both compressible and incompressible. To leading nontrivial order beyond the non-interacting high-temperature limit, they are determined analytically in terms of the Haldane pseudopotential parameters $V_m$, which provides a qualitative description of the crossover towards incompressible ground states for different filling factors. Moreover, we show that for contact interactions $\sim g_2 δ^{(2)}({\bf x})$, which are scale invariant at the classical level, the non-commutativity of the guiding center coordinates gives rise to a quantum anomaly in the commutator $i [\hat{H}_{\rm LLL}, \hat{D}_R] = (2 + \ell \partial_\ell) \hat{H}_{\rm LLL}$ with the dilatation operator $\hat{D}_R$ in the LLL, which replaces the trace anomaly in the absence of a magnetic field. The interaction-induced breaking of scale invariance gives rise to a finite frequency shift of the breathing mode in a harmonic trap, which describes transitions between different Landau levels, the strength of which is estimated in terms of the relevant dimensionless coupling constant $\tilde{g}_2$.

cond-mat.quant-gas↗

arXiv2022

Collective modes in interacting two-dimensional tomographic Fermi liquids

We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated "tomographic" transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless. We derive expressions for both the longitudinal and the transverse conductivity and discuss the collective mode spectrum along the collisionless-tomographic-hydrodynamic crossover. Longitudinal modes cross over from zero sound in the collisionless regime to hydrodynamic first sound in the tomographic and hydrodynamic regime, where odd-parity damping appears as a subleading correction to the lifetime. In charged Fermi liquids with long-range Coulomb coupling, these modes reduce to plasmons with a strongly suppressed odd-parity correction to the damping. The transverse response, by contrast, has a specific tomographic transport regime with two imaginary odd-parity modes, one of which requires a finite repulsive interaction, distinct from both the shear sound in the collisionless regime and an overdamped diffusive current mode in the hydrodynamic limit. Our work demonstrates that there are deep many-body aspects of interacting Fermi liquids, which are often thought to be well understood theoretically, remaining unexplored.

cond-mat.mes-hall↗

arXiv2022

Analytic approach to transport in superconducting junctions with arbitrary carrier density

Particle transport across Josephson junctions is commonly described using a simplifying approximation (often called the Andreev approximation), which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections, with no normal reflections, occur at interfaces. While this approximation is appropriate for superconductors with high carrier density (for which the chemical potential vastly exceeds the pairing gap), it breaks down for low-carrier-density superconductors, such as topological superconductors, doped semiconductors, or superfluid quantum gases. Here, we present a general $analytical$ framework for transport in superconducting junctions that does not rely on this limiting Andreev approximation. We apply our framework to describe transport in junctions between $s$-wave superconductors along the BCS-BEC crossover, which interpolates between the conventional high-carrier-density (BCS-)regime and moderate- as well as low-carrier-density regimes (unitary and BEC regimes), for which the Andreev approximation is not valid. As the system is tuned from the BCS to the BEC regime, the magnitude of a subgap current due to multiple Andreev reflections (MAR) decreases. However, nonlinearities in the current-voltage characteristic become more pronounced near the intermediate unitary limit, giving rise to sharp peaks and dips in the differential conductance with even $negative$ differential conductance at specific voltages. Microscopically, the negative differential conductance is related to the van Hove points in the band structures, at which enhanced normal reflection occurs and that become accessible only when the chemical potential is comparable to or smaller than the pairing gap. The subgap current due to MAR vanishes at a critical interaction strength on the BEC side, which we identify as the splitting point where the particle dispersion changes curvature.

cond-mat.mes-hall↗

arXiv2022

Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases

Two-dimensional Fermi gases with universal short-range interactions are known to exhibit a quantum anomaly, where a classical scale and conformal invariance is broken by quantum effects at strong coupling. We argue that in a quasi two-dimensional geometry, a conformal window remains at weak interactions. Using degenerate perturbation theory, we verify the conformal symmetry by computing the energy spectrum of mesoscopic particle ensembles in a harmonic trap, which separates into conformal towers formed by so-called primary states and their center-of-mass and breathing-mode excitations, the latter having excitation energies at precisely twice the harmonic oscillator energy. In addition, using Metropolis importance sampling, we compute the hyperradial distribution function of the many-body wave functions, which are predicted by the conformal symmetry in closed analytical form. The weakly interacting Fermi gas constitutes a system where the nonrelativistic conformal symmetry can be revealed using elementary methods, and our results are testable in current experiments on mesoscopic Fermi gases.

cond-mat.quant-gas↗

arXiv2022

Corrections to reaction-diffusion dynamics above the upper critical dimension

Reaction-diffusion models are common in many areas of statistical physics, where they describe the late-time dynamics of chemical reactions. Using a Bose gas representation, which maps the real-time dynamics of the reactants to the imaginary-time evolution of an interacting Bose gas, we consider corrections to the late-time scaling of $k$-particle annihilation processes $k A \to \emptyset$ above the upper critical dimension, where mean-field theory sets the leading order. We establish that the leading corrections are not given by a small renormalization of the reaction rate due to $k$-particle memory effects, but instead set by higher-order correlation functions that capture memory effects of sub-clusters of reactants. Drawing on methods developed for ultracold quantum gases and nuclear physics, we compute these corrections exactly for various annihilation processes with $k>2$.

cond-mat.stat-mech↗

arXiv2021

Probing embedded topological modes in bulk-like GeTe-Sb$_2$Te$_3$ heterostructures

The interface between topological and normal insulators hosts metallic states that appear due to the change in band topology. While these topological states at a surface, i.e., a topological insulator-air/vacuum interface, have been studied intensely, topological states at a solid-solid interface have been less explored. Here we combine experiment and theory to study such \textit{embedded} topological states (ETSs) in heterostructures of GeTe (normal insulator) and Sb$_2$Te$_3$ (topological insulator). We analyse their dependence on the interface and their confinement characteristics. To characterise the heterostructures, we evaluate the GeTe-Sb$_2$Te$_3$ band offset using X-ray photoemission spectroscopy, and chart the elemental composition using atom probe tomography. We then use first-principles to independently calculate the band offset and also parametrise the band structure within a four-band continuum model. Our analysis reveals, strikingly, that under realistic conditions, the interfacial topological modes are delocalised over many lattice spacings. Interestingly, the first-principles calculations indicate that the ETSs are relatively robust to disorder and this may have practical ramifications. Our study provides insights into how to manipulate topological modes in heterostructures and also provides a basis for recent experimental findings [Nguyen \textit{et al.}, Sci. Rep. \textbf{6}, 27716 (2016)] where ETSs were seen to couple over large distances.

cond-mat.mes-hall↗

arXiv2021

Electromagnetic response of composite Dirac fermions in the half-filled Landau level

An effective field theory of composite Dirac fermions was proposed by Son [Phys. Rev. X 5, 031027 (2015)] as a theory of the half-filled Landau level with explicit particle-hole symmetry. We compute the electromagnetic response of this Son-Dirac theory on the level of the random phase approximation (RPA), where we pay particular attention to the effect of an additional composite-fermion dipole term that is needed to restore Galilean invariance. We find that once this dipole correction is taken into account, spurious interband transitions and collective modes that are present in the response of the unmodified theory either cancel or are strongly suppressed. We demonstrate that this gives rise to a consistent theory of the half-filled Landau level valid at all frequencies, at least to leading order in the momentum. In addition, the dipole contribution modifies the Fermi-liquid response at small frequency and momentum, which is a prediction of the Son-Dirac theory within the RPA that distinguishes it from a separate description of the half-filled Landau level by Halperin, Lee, and Read within the RPA.

cond-mat.str-el↗

arXiv2021

Hydrodynamics of a superfluid smectic

We determine the hydrodynamic modes of the superfluid analog of a smectic-A phase in liquid crystals, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose-Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin-orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.

cond-mat.quant-gas↗

arXiv2021

libtxsize -- a library for automated Bitcoin transaction-size estimates

This paper presents libtxsize, a library to estimate the size requirements of arbitrary Bitcoin transactions. To account for different use cases, the library provides estimates in bytes, virtual bytes, and weight units. In addition to all currently existing input, output, and witness types, the library also supports estimates for the anticipated Pay-to-Taproot transaction type, so that estimates can be used as input for models attempting to quantify the impact of Taproot on Bitcoin's scalability. libtxsize is based on analytic models, whose credibility is established through first-principle analysis of transaction types as well as exhaustive empirical validation. Consequently, the paper can also serve as reference for different Bitcoin data and transaction types, their semantics, and their size requirements (both from an analytic and empirical point of view).

cs.DC↗

arXiv2021

Universal relations for dipolar quantum gases

We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances. The only relevant parameters are the dipole length as well as the scattering length of the combined short-range plus dipolar interaction potential. We derive adiabatic relations that link the change in the thermodynamic potentials with respect to the scattering length and the dipole length to a generalized Tan contact parameter and a new dipolar contact, which involves an integral of a short-distance regularized pair distribution function. These two quantities determine the scale anomaly in the difference between pressure and energy density and also the internal energy in the presence of a harmonic confinement. For a weak transverse confinement, configurations with attractive interactions appear, which lead to a density-wave instability beyond a critical strength of the dipolar interaction. We show that this instability essentially coincides with the onset of a roton minimum in the excitation spectrum and may be understood in terms of a quantum analog of the Hansen-Verlet criterion for freezing of a classical fluid.

cond-mat.quant-gas↗

arXiv2020

Understanding HPC Benchmark Performance on Intel Broadwell and Cascade Lake Processors

Hardware platforms in high performance computing are constantly getting more complex to handle even when considering multicore CPUs alone. Numerous features and configuration options in the hardware and the software environment that are relevant for performance are not even known to most application users or developers. Microbenchmarks, i.e., simple codes that fathom a particular aspect of the hardware, can help to shed light on such issues, but only if they are well understood and if the results can be reconciled with known facts or performance models. The insight gained from microbenchmarks may then be applied to real applications for performance analysis or optimization. In this paper we investigate two modern Intel x86 server CPU architectures in depth: Broadwell EP and Cascade Lake SP. We highlight relevant hardware configuration settings that can have a decisive impact on code performance and show how to properly measure on-chip and off-chip data transfer bandwidths. The new victim L3 cache of Cascade Lake and its advanced replacement policy receive due attention. Finally we use DGEMM, sparse matrix-vector multiplication, and the HPCG benchmark to make a connection to relevant application scenarios.

cs.PF↗

arXiv2020

High-temperature expansion of the viscosity in interacting quantum gases

We compute the frequency-dependent shear and bulk viscosity spectral functions of an interacting Fermi gas in a quantum virial expansion up to second quadratic order in the fugacity parameter $z=e^{βμ}$, which is small at high temperatures. Calculations are carried out using a diagrammatic finite-temperature field-theoretic framework, in which the analytic continuation from Matsubara to real frequencies is carried out in closed analytic form. Besides a possible zero-frequency Drude peak, our results for the spectral functions show a broad continuous spectrum at all frequencies with an additional bound-state contribution for frequencies larger than the dimer-breaking energy. Our results are consistent with various sum rules and universal high-frequency tails. In the low-frequency limit, the shear viscosity spectral function is recast as a collision integral, which reproduces known results for the static shear viscosity from kinetic theory. Our findings for the static bulk viscosity of a Fermi gas near unitarity, however, show a nonanalytic dependence on the scattering length, at variance with kinetic theory.

cond-mat.quant-gas↗

arXiv2019

Quantum oscillations in Dirac magnetoplasmons

The plasmon frequency in standard electron gases with a parabolic single-particle dispersion is a purely classical quantity that is not sensitive to electron interactions or the equation of state. We demonstrate that this canonical result no longer holds for plasmons in three-dimensional semimetals, which can thus be used to probe many-body effects in these systems. In particular, we show that the plasmon frequency in an external magnetic field displays quantum oscillations, which is not the case for the electron gas. Using the random phase approximation, results are presented for the magnetoplasmon dispersion and the loss function in Dirac semimetals. We include a full discussion of the loss function in a magnetic field as a function of the direction of propagation with respect to the magnetic field direction and discuss the transition from large magnetic fields to the low-field limit.

cond-mat.mes-hall↗

arXiv2019

Bridging the Architecture Gap: Abstracting Performance-Relevant Properties of Modern Server Processors

We describe a universal modeling approach for predicting single- and multicore runtime of steady-state loops on server processors. To this end we strictly differentiate between application and machine models: An application model comprises the loop code, problem sizes, and other runtime parameters, while a machine model is an abstraction of all performance-relevant properties of a CPU. We introduce a generic method for determining machine models and present results for relevant server-processor architectures by Intel, AMD, IBM, and Marvell/Cavium. Considering this wide range of architectures, the set of features required for adequate performance modeling is surprisingly small. To validate our approach, we compare performance predictions to empirical data for an OpenMP-parallel preconditioned CG algorithm, which includes compute- and memory-bound kernels. Both single- and multicore analysis shows that the model exhibits average and maximum relative errors of 5% and 10%. Deviations from the model and insights gained are discussed in detail.

cs.DC↗

arXiv2018

Tunable surface plasmons in Weyl semimetals TaAs and NbAs

By means of high-resolution electron energy loss spectroscopy, we investigate the low-energy excitation spectrum of transition-metal monopnictides hosting Weyl fermions. We observe gapped plasmonic modes in (001)-oriented surfaces of single crystals of NbAs and TaAs at 66 and 68 meV, respectively. Our findings are consistent with theory and we estimate an effective Coulomb interaction strength $α_{\rm eff}\approx0.41$ for both samples. We also demonstrate that the modification of the surface of transition-metal monopnictides by the adsorption of chemical species (in our case, oxygen and hydrocarbon fragments) changes the frequency of the plasmonic excitations, with a subsequent modification of the effective interaction strength in the 0.30-0.48 range. The remarkable dependence of plasmonic features on the presence of adsorbates paves the way for plasmonic sensors based on Weyl semimetals operating in the mid-infrared.

cond-mat.mes-hall↗

arXiv2018

Automated Instruction Stream Throughput Prediction for Intel and AMD Microarchitectures

An accurate prediction of scheduling and execution of instruction streams is a necessary prerequisite for predicting the in-core performance behavior of throughput-bound loop kernels on out-of-order processor architectures. Such predictions are an indispensable component of analytical performance models, such as the Roofline and the Execution-Cache-Memory (ECM) model, and allow a deep understanding of the performance-relevant interactions between hardware architecture and loop code. We present the Open Source Architecture Code Analyzer (OSACA), a static analysis tool for predicting the execution time of sequential loops comprising x86 instructions under the assumption of an infinite first-level cache and perfect out-of-order scheduling. We show the process of building a machine model from available documentation and semi-automatic benchmarking, and carry it out for the latest Intel Skylake and AMD Zen micro-architectures. To validate the constructed models, we apply them to several assembly kernels and compare runtime predictions with actual measurements. Finally we give an outlook on how the method may be generalized to new architectures.

cs.PF↗

arXiv2018

On the accuracy and usefulness of analytic energy models for contemporary multicore processors

This paper presents refinements to the execution-cache-memory performance model and a previously published power model for multicore processors. The combination of both enables a very accurate prediction of performance and energy consumption of contemporary multicore processors as a function of relevant parameters such as number of active cores as well as core and Uncore frequencies. Model validation is performed on the Sandy Bridge-EP and Broadwell-EP microarchitectures. Production-related variations in chip quality are demonstrated through a statistical analysis of the fit parameters obtained on one hundred Broadwell-EP CPUs of the same model. Insights from the models are used to explain the performance- and energy-related behavior of the processors for scalable as well as saturating (i.e., memory-bound) codes. In the process we demonstrate the models' capability to identify optimal operating points with respect to highest performance, lowest energy-to-solution, and lowest energy-delay product and identify a set of best practices for energy-efficient execution.

cs.PF↗