arXiv subjects

Thomas Blommel

Publications and source records attributed to Thomas Blommel.

8 recordsLinked to original sources

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↗

arXiv2026

Influence of Markovianity and self-consistency on time-resolved spectral functions of driven quantum systems

We present a systematic comparison of the real-time Dyson expansion (RTDE) with established non-equilibrium Green's function approaches for simulating driven, interacting quantum systems. Focusing on density matrix dynamics, time-off-diagonal Green's functions, and time-resolved photoemission spectra, we benchmark RTDE against fully self-consistent Kadanoff-Baym equation (KBE) calculations, the generalized Kadanoff-Baym ansatz (GKBA), and exact diagonalization for small systems using second order many-body perturbation theory. Using a driven two-band Hubbard model, we show that mean-field single particle density matrix trajectories provide a reliable baseline for RTDE across a broad range of interaction strengths and excited-carrier populations. Further, RTDE accurately captures correlation effects in the Green's functions, including long-lived oscillations and revivals that are strongly suppressed by the overdamping inherent to self-consistent KBE schemes. As a consequence, RTDE resolves rich non-equilibrium spectral structure in time-resolved photoemission, such as interaction- and population-dependent quasiparticle splittings and bandgap renormalization, which are largely washed out in self-consistent approaches, yet are present in the exact solutions. Our results demonstrate that RTDE bridges the gap between mean-field propagation and full two-time KBE simulations, retaining favorable linear scaling while capturing essential dynamical correlations relevant for ultrafast spectroscopy.

cond-mat.str-el↗

arXiv2025

Many-Body Perturbation Theory for Driven Dissipative Quasiparticle Flows and Fluctuations

We present a unified many-body perturbation theory for open quantum systems, that treats dissipation, correlations, and external driving on equal footing. Using a Keldysh-Lindblad formalism, we introduce diagrammatic treatment of dissipative interaction lines representing quasiparticle flows and fluctuations. Two new Feynman rules render the evaluation of dissipative diagrams compact and systematically improvable, while preserving the Keldysh and anti-Hermitian symmetries of the closed-system theory. Consequently, the structure of the Kadanoff-Baym equations (KBE) remains unchanged, enabling existing numerical methods to be directly applied. To illustrate this, we derive dissipative versions of the second Born and $GW$ approximations, identifying the physical content of the self-energy components. Moreover, we demonstrate that time-linear approximations to the full KBE retain their closed structure and can be efficiently used to simulate relaxation and decoherence dynamics. The impact of dissipation-induced correlations is illustrated in the driven Haldane model, where quasiparticles exhibit nontrivial stabilization and acquire lifetimes that far exceed those of the bare system. This framework establishes a general route toward first-principles modeling of correlated, driven, and dissipative quantum materials.

cond-mat.str-el↗

arXiv2025

A Unified Simulation Framework for Correlated Driven-Dissipative Quantum Dynamics

Time-resolved photoemission spectroscopy provides a unique and direct way to explore the real-time nonequilibrium dynamics of electrons and holes. The formal theory of the spectral function evolution requires inclusion of electronic correlations and dissipation, which are challenging due to the associated long simulation timescales which translate to a high computational cost. Recent methodological developments, namely the Real-Time Dyson Expansion, as well as theoretical developments of many-body perturbation theory for dissipative systems, have allowed for the study of driven-dissipative interacting quantum systems. In this work, we implement the hitherto unrealized study of driven-dissipative interacting quantum systems which includes driven dynamical correlations and utilizes these new methods and perturbative expansions. We illustrate the combined formalism on a prototypical two-band semiconductor model with long-range density-density Coulomb interactions. We show that the intraband thermalization of conduction band electrons induces nontrivial time-dependent changes in the system's bandstructure and a time-evolving band-gap renormalization (with a reduction by up to 10\%). We show that the qualitative features are preserved for a variety of parameters, discuss the corresponding spectral dynamics, and provide an outlook on the newly introduced simulation framework, which enables treating electron-electron scattering and dissipation effects on equal footing.

cond-mat.mtrl-sci↗

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

Adaptive Time Stepping for the Two-Time Integro-Differential Kadanoff-Baym Equations

The non-equilibrium Green's function gives access to one-body observables for quantum systems. Of particular interest are quantities such as density, currents, and absorption spectra which are important for interpreting experimental results in quantum transport and spectroscopy. We present an integration scheme for the Green's function's equations of motion, the Kadanoff-Baym equations (KBE), which is both adaptive in the time integrator step size and method order as well as the history integration order. We analyze the importance of solving the KBE self-consistently and show that adapting the order of history integral evaluation is important for obtaining accurate results. To examine the efficiency of our method, we compare runtimes to a state of the art fixed time step integrator for several test systems and show an order of magnitude speedup at similar levels of accuracy.

physics.comp-ph↗

arXiv2024

Chirped amplitude mode in photo-excited superconductors

Using a state-of-the-art numerical scheme, we show that the Higgs mode under excitation exhibits chirped oscillations and exponential decay when fluctuations are included. This is in stark contrast to conventional BCS collisionless dynamics which predict power-law decay and the absence of chirping. The chirped amplitude mode enables us to determine the local modification of the effective potential even when the system is in a long-lived prethermal state. We then show that this chirped amplitude mode is an experimentally observable quantity since the photoinduced (super)current in pump-probe experiments serves as an efficient proxy for the order parameter dynamics, including the chirped dynamics. Our result is based on the attractive Hubbard model using dynamical mean-field theory within the symmetry-broken state after a excitation across the superconducting gap. Since the collective response involves long timescales, we extend the hierarchical low-rank compression method for nonequilibrium Green's functions to symmetry-broken states and show that it serves as an efficient representation despite long-lived memory kernels.

cond-mat.supr-con↗

arXiv2017

Integer Lattice Gas with Monte Carlo collision operator recovers the entropic lattice Boltzmann method with Poisson distributed fluctuations

We are examining a new kind of lattice gas that closely resembles modern lattice Boltzmann methods. This new kind of lattice gas, that we call a Monte Carlo Lattice Gas, has interesting properties that shed light on the origin of the multi-relaxation time collision operator and it derives the equilibrium distribution for entropic lattice Boltzmann. Furthermore these lattice gas methods have Galilean invariant fluctuations given by a Poisson statistics, giving further insight into the properties that we should expect for fluctuating lattice Boltzmann methods.

physics.comp-ph↗