arXiv subjects

Emanuel Gull

Publications and source records attributed to Emanuel Gull.

At least 19 recordsLinked to original sources

arXiv2026

Compact and Stable Representation of Real-Frequency Spectral Functions for Machine Learning

We introduce a compact and stable moment representation for real-frequency Green's functions, hybridization functions, and self-energies for machine-learning applications, avoiding the inefficiency of dense frequency grids as well as the ill-posed analytic continuation of Matsubara approaches. The representation is constructed from Cayley-mapped trigonometric moments with the Jacobian included, which preserve spectral-weight normalization, tie the moment sequence to a positive matrix-valued spectral measure, and admit a systematic route to a pole representation via ESPRIT. This provides a fixed-dimensional learning target in which physical constraints such as normalization and positivity can be imposed directly. Using a graph-attention neural network with FiLM conditioning, we benchmark the representation on single-orbital DMFT, antiferromagnetic DMFT, and a two-orbital impurity model. The results demonstrate accuracy matching or exceeding that of direct frequency-domain learning, reliable reproduction of the density and staggered magnetization, stable self-energy reconstruction through Dyson equation inversion, and accurate recovery of matrix-valued spectra with orbital mixing.

physics.comp-ph↗

arXiv2026

Hybrid Hamiltonian-diagrammatic quantum impurity solver

Quantum impurity models, which describe the coupling between interacting orbitals and a non-interacting bath, play a central role in the physics of strongly correlated electron systems. Solving a quantum impurity model in general requires the use of non-perturbative numerical methods. Hamiltonian-based approaches, which rely on an explicit bath discretization, are typically limited to a small number of bath sites or small entanglement, and diagrammatic methods suffer from sign problems, slow convergence, or diagram truncation approximations. Here we show that these two classes of methods can be combined: augmenting diagrammatic methods with a small auxiliary bath can reduce the residual problem to a regime where low-order perturbation theory is highly accurate and rapidly converging. In a simple benchmark, the precision of the hybrid approach surpasses bold-line calculations by several orders of magnitude; for a strongly interacting two-orbital model with a severe sign problem, convergence is achieved at three orders of magnitude lower computational cost than competing methods; and convergence to the unknown exact result is rapidly accelerated in a difficult realistic problem. Our results establish a practical route to high-precision quantum impurity solutions in correlated quantum systems.

cond-mat.str-el↗

arXiv2026

Validity and Limits of Low Order Hybridization Expansion Approaches for Multi-Orbital Systems

Low-order hybridization expansion methods such as the non-crossing approximation (NCA) and the one-crossing approximation (OCA) are widely used impurity solvers in the study of strongly correlated systems, yet their accuracy in genuine multi-orbital settings remains poorly understood. Using the decoupled orbital limit as a controlled reference point, we derive analytic results connecting multi-orbital restricted propagators and Green's functions to their single-orbital counterparts, identify the diagrammatic mechanisms responsible for the breakdown of low-order methods in multi-orbital settings, and determine their regimes of applicability. Our central finding is that the accuracy of these methods is governed by the least correlated orbital: i.e., the orbital with the most rapidly decaying retarded Green's function. That orbital's properties are transferred to all other orbitals through a spurious coupling generated by the truncated expansion, thereby suppressing correlation-induced features such as the Kondo resonance. This occurs even in orbitals that are themselves strongly correlated within single-orbital calculations using the same approximation scheme. We confirm this numerically across representative two-orbital model systems in the steady-state, systematically identifying the parameter regimes in which low-order methods succeed or fail. Our results provide a practical guide for assessing when insights from single-orbital calculations carry over to multi-orbital settings, and serve as a benchmark for the development and validation of higher-order multi-orbital impurity solvers.

cond-mat.str-el↗

arXiv2026

Evolution of the Saddle Point in Antimony Telluride Homologous Superlattices

Combining topological insulators with topological semimetals in the form of homologous superlattices is a promising approach for generating correlated quantum matter based upon Fermi level alignment with band extrema. For antimony telluride, a saddle point is predicted to occur at the M-point, while antimonene layering is predicted to move the M-point valence band towards the Fermi level. To date, the predicted saddle point at the M-point has not yet been demonstrated, and studies of antimony telluride homologous superlattices have been limited to one or two layers of antimonene added to antimony telluride. Here, we present scanning tunneling spectroscopy and angle-resolved photoemission spectroscopy studies of a series of antimony telluride homologous superlattices with two to four layers of antimonene. In addition to demonstrating the presence of a saddle point and associated van Hove singularity near the M-point, we identify the key role of Sb and Te $p_z$ orbital hybridization in driving the van Hove singularity toward the Fermi level.

cond-mat.mtrl-sci↗

arXiv2026

H-NESSi: The Hierarchical Non-Equilibrium Systems Simulation package

We present H-NESSi (The Hierarchical Non-Equilibrium Systems Simulation package), an open-source software package for solving the Kadanoff-Baym equations (KBE) of nonequilibrium Green's function (NEGF) theory using hierarchical low-rank compression techniques. The simulation of strongly correlated quantum systems out of equilibrium is severely limited by the cubic scaling in propagation time and quadratic memory growth associated with conventional two-time formulations. H-NESSi overcomes these limitations by combining high-order time-stepping schemes with hierarchical off-diagonal low-rank (HODLR) representations of the retarded and lesser Green's functions, enabling controllable accuracy at substantially reduced computational cost and memory usage. Imaginary time quantities are efficiently represented using the discrete Lehmann representation (DLR), allowing compact and accurate treatment of thermal initial states. The implementation supports multiorbital systems, adaptive singular value truncation, and both shared-memory (OpenMP) and distributed-memory (MPI) parallelization strategies suitable for large-scale lattice calculations. The workflow closely mirrors established NEGF frameworks while introducing compression transparently into the propagation procedure. Benchmark applications to driven superconductors within dynamical mean-field theory and to the two-dimensional Hubbard model demonstrate favorable scaling compared to conventional implementations, with asymptotic time complexity significantly below the cubic scaling of uncompressed approaches. H-NESSi thus enables long-time and large-system nonequilibrium simulations of correlated quantum materials which were previously computationally prohibitive.

cond-mat.str-el↗

arXiv2025

Multi-orbital dynamical mean-field theory with a complex-time solver

We present the combination of a complex-time tensor-network impurity solver with an analytic continuation scheme based on exponential fitting as an efficient framework for single and multi-orbital dynamical mean-field calculations. By performing time-evolution along a complex-time contour, the approach balances computational cost with the difficulty of spectral recovery, offering greater flexibility than methods confined to the real or imaginary axis. By complementing the complex-time evolution with an exponential fitting scheme, we faithfully extract real-time information at negligible cost. The resulting method obtains high-resolution spectra at a significantly lower computational cost than real-time evolution, offering a promising tool for ab initio studies of strongly correlated materials.

cond-mat.str-el↗

arXiv2025

Global approximations to correlation functions of strongly interacting quantum field theories

We introduce a method for constructing global approximations to correlation functions of strongly interacting quantum field theories, starting from perturbative results. The key idea is to employ interpolation method, such as the two-point Pad\'e expansion, to interpolate the weak and strong coupling expansions of correlation function. We benchmark this many-body interpolation approach on two prototypical models: the lattice $\phi^4$ field theory and the 2D Hubbard model. For the $\phi^4$ theory, the resulting two point Pad\'e approximants exhibit uniform and global convergence to the exact correlation function. For the Hubbard model, we show that even at second order, the Pad\'e appproximant already provides reasonable characterization of the Matsubara Green's function for a wide range of parameters. Finally, we offer a heuristic explanation for these convergence properties based on analytic function theory.

cond-mat.str-el↗

arXiv2025

Discovering topological phases in gray-Tin

Non-trivial topological phases often emerge in narrow-gap semiconductors with a delicate blend of spin-orbit coupling and electron correlation. The diamond-lattice allotrope of Sn ($\alpha$-Sn) exemplifies this behavior, hosting multiple topological phases that can be tuned by small distortions in the lattice. Despite rapid experimental progress, theoretical descriptions of $\alpha$-Sn lack predictive power and rely mainly on tight-binding models and density functional theory with uncontrolled approximations. We employ first-principles fully self-consistent, relativistic GW (scGW) to overcome these limitations. The scGW recovers the experimentally observed zero-gap semiconductor and the strain-induced topological insulator and Dirac semimetal phases, while also predicting new trivial and topological insulators and a Dirac semimetal phase, further demonstrating the versatility of $\alpha$-Sn for band engineering. Additionally, we propose a robust diagnostic of topological behavior based on a combined analysis of band and orbital-occupation dispersions, tailored for correlated methods where standard mean-field-based topological invariants fall short. Our findings pave the way for studying a broad class of topological materials using accurate first-principles methods beyond density functional theory.

cond-mat.str-el↗

arXiv2025

Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.

cond-mat.str-el↗

arXiv2025

Inchworm tensor train hybridization expansion quantum impurity solver

The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing accurate results for multi-orbital systems with complex interactions and off-diagonal hybridizations. Recently, tensor-train-based integration and summation techniques have shown promise as effective alternatives. In this study, we use tensor train methods to tackle quantum impurity problems formulated within the imaginary-time inchworm hybridization expansion framework. We identify key challenges in the inchworm expansion itself and its interplay with tensor-train-based methods. We demonstrate the accuracy and versatility of our approach by solving general quantum impurity problems. Our results suggest that tensor-train decomposition schemes offer a viable path toward accurate and efficient multi-orbital impurity solvers.

cond-mat.str-el↗

arXiv2025

Minimal pole representation for spectral functions

Representing spectral densities, real-frequency, and real-time Green's functions of continuous systems by a small discrete set of complex poles is an ubiquitous problem in condensed matter physics, with applications ranging from quantum transport simulations to the simulation of strongly correlated electron systems. This paper introduces a method for obtaining a compact, approximate representation of these functions, based on their parameterization on the real axis and a given approximate precision. We show applications to typical spectral functions and results for structured and unstructured correlation functions of model systems.

cond-mat.str-el↗

arXiv2024

Minimal pole representation and analytic continuation of matrix-valued correlation functions

We present a minimal pole method for analytically continuing matrix-valued imaginary frequency correlation functions to the real axis, enabling precise access to off-diagonal elements and thus improving the interpretation of self-energies and susceptibilities in quantum simulations. Traditional methods for matrix-valued analytic continuation tend to be either noise-sensitive or make ad-hoc positivity assumptions. Our approach avoides these issues via the construction of a compact pole representation with shared poles through exponential fits, expanding upon prior work focused on scalar functions. We test our method across various scenarios, including fermionic and bosonic response functions, with and without noise, and for both continuous and discrete spectra of real materials and model systems. Our findings demonstrate that this technique addresses the shortcomings of existing methodologies, such as artificial broadening and positivity violations. The paper is supplemented with a sample implementation in Python.

cond-mat.str-el↗

arXiv2024

Pairing boost from enhanced spin-fermion coupling in the pseudogap regime

We perform a fluctuation analysis of the pairing interaction in the hole-doped Hubbard model within the dynamical cluster approximation. Our analysis reveals that spin-fluctuation-mediated pairing differs qualitatively in the over- and underdoped regimes. In the underdoped regime, spin fluctuations open a pseudogap. We show that in this regime the spin-fermion coupling mediates a giant attraction between antinodal fermions. This explains why superconductivity survives at underdoping in the Hubbard model and cuprates, despite the lack of coherent fermionic quasiparticles in the pseudogap regime.

cond-mat.str-el↗

arXiv2024

Nonequilibrium Steady State Full Counting Statistics in the Noncrossing Approximation

Quantum transport is often characterized not just by mean observables like the particle or energy current, but by their fluctuations and higher moments, which can act as detailed probes of the physical mechanisms at play. However, relatively few theoretical methods are able to access the full counting statistics (FCS) of transport processes through electronic junctions in strongly correlated regimes. While most experiments are concerned with the steady state properties, most accurate theoretical methods rely on computationally expensive propagation from a tractable initial state. Here, we propose a simple approach for computing the FCS through a junction directly at the steady state, utilizing the propagator noncrossing approximation (NCA). Compared to time propagation, our method offers reduced computational cost at the same level of approximation; but the idea can also be used within other approximations or as a basis for numerically exact techniques. We demonstrate the method's capabilities by investigating the impact of lead dimensionality on electronic transport in the nonequilibrium Anderson impurity model at the onset of Kondo physics. Our results reveal a distinct signature of one dimensional leads in the noise and Fano factor not present for other dimensionalities, showing the potential of FCS measurements as a probe of the environment surrounding a quantum dot.

cond-mat.mes-hall↗

arXiv2024

Feynman diagrammatics based on discrete pole representations: A path to renormalized perturbation theories

By merging algorithmic Matsubara integration with discrete pole representations we present a procedure to generate fully analytic closed form results for impurity problems at fixed perturbation order. To demonstrate the utility of this approach we study the Bethe lattice and evaluate the second order self-energy for which reliable benchmarks exist. We show that, when evaluating diagrams on the Matsubara axis, the analytic sums of pole representations are extremely precise. We point out the absence of a numerical sign problem in the evaluation, and explore the application of the same procedure for real-frequency evaluation of diagrams. We find that real-frequency results are subject to noise that is controlled at low temperatures and can be mitigated at additional computational expense. We further demonstrate the utility of this approach by evaluating dynamical mean-field and bold diagrammatic self-consistency schemes at both second and fourth order and compare to benchmarks where available.

cond-mat.str-el↗

arXiv2024

Steady-state properties of multi-orbital systems using quantum Monte Carlo

A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.

cond-mat.mes-hall↗

arXiv2024

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarizes the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations.

cond-mat.mtrl-sci↗

arXiv2024

Symmetry adaptation for self-consistent many-body calculations

The exploitation of space group symmetries in numerical calculations of periodic crystalline solids accelerates calculations and provides physical insight. We present results for a space-group symmetry adaptation of electronic structure calculations within the finite-temperature self-consistent GW method along with an efficient parallelization scheme on accelerators. Our implementation employs the simultaneous diagonalization of the Dirac characters of the orbital representation. Results show that symmetry adaptation in self-consistent many-body codes results in substantial improvements of the runtime, and that block diagonalization on top of a restriction to the irreducible wedge results in additional speedup.

physics.comp-ph↗