NESSi

Official Resources

• Homepage: https://nessi.tuxfamily.org/
• Repository: https://github.com/nessi-project (or SourceForge)
• License: GNU General Public License v3.0

Overview

NESSi (Non-Equilibrium Systems Simulation) is an open-source C++ framework designed for the simulation of non-equilibrium quantum dynamics using the Kadanoff-Baym contour formalism. Unlike standard steady-state NEGF codes, NESSi explicitly works in the time domain, solving for the two-time Green's functions $G(t, t')$. This allows for the study of ultrafast phenomena, transient transport, and the relaxation dynamics of strongly interacting quantum systems driven by external fields.

Scientific domain: Ultrafast Dynamics, Many-Body Physics, Time-Dependent Transport Target user community: Physicists studying non-equilibrium phases, optical control, and transient spectroscopy

Theoretical Methods

• Kadanoff-Baym Equations (KBE): Time propagation of the non-equilibrium Green's function on the L-shaped contour.
• Many-Body Approximations:
  • Hartree-Fock (HF).
  • Second Born Approximation (2B).
  • GW approximation.
  • T-Matrix approximations.
• Interaction Types:
  • Hubbard U (electron-electron).
  • Holstein model (electron-phonon).

Capabilities

• Simulations:
  • Pump-probe spectroscopy experiments.
  • Quench dynamics.
  • Transient current in molecular junctions.
• Observables:
  • Time-resolved spectral functions $A(t, \omega)$.
  • Occupations and currents.
  • Energy conservation checks.
• Systems:
  • Lattice models (Hubbard, Holstein).
  • Single Anderson Impurity Model (SIAM).

Key Strengths

• Rigorous Dynamics: Treats initial correlations and memory effects exactly within the chosen approximation (unlike GKBA which neglects some memory).
• Modularity: The software is structured as a library (libnessi), separating the Green's function data structures from the physical model implementation.
• High-Order Solvers: Advanced time-stepping algorithms for integro-differential equations.

Inputs & Outputs

• Inputs:
  • Model parameters (hopping, U, coupling strength).
  • Time grid and contour definitions.
  • Initial state configuration.
• Outputs:
  • Two-time Green's functions (binary/HDF5).
  • Post-processed spectral data.

Interfaces & Ecosystem

• Libraries: Depends on GSL, FFTW, MPI.
• Usage: Typically used to write specific solver executables for a given model Hamiltonian.

Performance Characteristics

• Computational Cost: Scaling is $O(N_t^3)$ due to the two-time nature (memory effects), making it much more expensive than time-local methods (GKBA or TD-DFT).
• Parallelism: MPI parallelization over momentum/k-points or orbital blocks.

Limitations & Known Constraints

• Time Limits: The cubic scaling limits simulations to relatively short physical times.
• System Size: Primarily suited for model Hamiltonians or small clusters; atomistic full-basis simulations are extremely costly in full KBE.

Comparison with Other Codes

• vs. TD-DFT: TD-DFT is cheaper ($O(N_t)$) but often lacks memory effects and sophisticated correlation; NESSi captures lifetime effects and non-Markovian dynamics.
• vs. CHEERS: Another KBE solver; NESSi focuses on providing a C++ library infrastructure.

Community and Support

• Development: Developed by Michael Schüler, Denis Golez, and collaborators (Graz/Fribourg).
• Documentation: Extensive Wiki and examples.

Verification & Sources

• Repository: https://nessi.tuxfamily.org
• Primary Publication: M. Schüler et al., Comp. Phys. Comm. 257, 107484 (2020).
• Verification status: ✅ VERIFIED
  • Published and documented research code.