.. _applications: **Applications based on TRIQS** ############################### The TRIQS library provides all the necessary building blocks for the development of applications for the study of interacting quantum systems. These applications can be grouped into one of the following categories: * **Official applications** These applications have readily been developed and are maintained by the TRIQS collaboration. * **External applications** These applications were developed and are maintained externally but are still fundamentally relying on TRIQS library features. * **Interfaces to external codes** These applications are thin wrappers around TRIQS independent codes that are developed and maintained externally. The maintenance of the interface layer is commonly shared between the TRIQS collaboration and the external developers. If you would like to have your application listed please contact us directly. .. _impurity_solvers: **Impurity Solvers** ==================== **Hybridization-expansion solver** ---------------------------------- The hybridization-expansion solver is an official TRIQS application that allows to solve the generic problem of a quantum impurity embedded in a conduction bath. It is based on a quantum Monte Carlo algorithm that stochastically samples the diagrams of a hybridization expansion of the partition function. For publications based on results produced with this application please cite `Comput. Phys. Comm. 200, 274 (2016) `_ *Homepage:* ``_ **Segment Picture Hybridization-expansion solver** -------------------------------------------------- The segment picture hybridization-expansion solver can solve quantum impurity models with local Hamiltonians that commute with the impurity density operators. When applicable, this algorithm is more efficient than the vanilla hybridization-expansion. In addition to a static local Hamiltonian, dynamic density-density and spin-spin interactions can be included. *Homepage:* ``_ **Interaction-expansion solver** -------------------------------- The interaction-expansion solver is an official TRIQS application that allows to solve the generic problem of a quantum impurity embedded in a conduction bath for an arbitrary local interaction vertex. It is based on a continuous-time quantum Monte Carlo algorithm that stochastically samples the diagrams of a weak-coupling expansion of the partition function in powers of the interaction (CT-INT). For publications based on results produced with this application please cite `10.5281/zenodo.15598402 `_ *Homepage:* ``_ **X-Crossing Approximation (XCA) solver** ----------------------------------------- The X-Crossing Approximation solver is an official TRIQS application that solves generic multiband Anderson impurity problems approximately through a perturbative (bold) expansion in the coupling to the bath, i.e. the hybridization function. It leverages a sum-of-exponentials representation together with the Discrete Lehmann Representation to achieve a parametrically better computational complexity than direct integration. For publications based on results produced with this application please cite `Phys. Rev. X 14, 031034 (2024) `_ and `SciPost Phys. 19, 121 (2025) `_ *Homepage:* ``_ **Hubbard I solver** -------------------- This solver gives the Hubbard I solution of a quantum impurity problem, i.e. it solves the atomic limit. This simple approximation allows for very quick answers even for large multiband systems. *Homepage:* ``_ **Hartree Fock solver** ----------------------- This solver calculates the self-consistent Hartree or Hartree Fock approximation for a given quantum impurity or lattice problem. It uses gradient descent to solve the self-consistency at fixed density or chemical potential. The solver is limited to static and local interactions. *Homepage:* ``_ **gem - Gutzwiller Embedding Method** ------------------------------------- gem is an official TRIQS application implementing the ghost Gutzwiller approximation (ghost-GA), a quantum embedding method that augments the Gutzwiller variational approach with auxiliary ("ghost") degrees of freedom. These additional bath levels systematically improve the description of the local spectral function and quasiparticle properties of correlated electron systems beyond the standard Gutzwiller approximation. *Homepage:* ``_ **PYED - Exact diagonalization for finite quantum systems (external)** ---------------------------------------------------------------------- The TRIQS-based python application pyed implements exact diagonalization for finite fermionic many-body quantum systems, together with calculations of several response functions in imagianary time. *Homepage*: ``_ **Interface to the pomerol exact diagonalization solver (external)** -------------------------------------------------------------------- TRIQS wrapper around the `Pomerol `_ exact diagonalization library. For publications based on results produced with this application please cite `10.5281/zenodo.592291 `_ *Homepage*: ``_ **Interface to the EDIpack impurity solver** -------------------------------------------------- This application provides an interface to the Lanczos-based exact diagonalization impurity solver `EDIpack `_. For publications based on results produced with this application please cite `SciPost Phys. Codebases 58 (2025) `_ and `Comput. Phys. Commun. 273, 108261 (2022) `_ *Homepage*: ``_ **Interface to the w2dynamics impurity solver** ----------------------------------------------- This application provides an interface to the continuous-time hybridization expansion impurity solver contained in the `w2dynamics `_ software package. For publications based on results produced with this application please cite `Comput. Phys. Commun. 235, 388 (2019) `_ *Homepage*: ``_ **Interface to the NRG Ljubljana impurity solver** -------------------------------------------------- This application provides an interface to the numerical renormalization group impurity solver `NRG Ljubljana `_. For publications based on results produced with this application please cite `Phys. Rev. B 79, 085106 (2009) `_ *Homepage*: ``_ .. _abinitio_tools: **Ab-Initio Tools** =================== **DFT tools - Toolbox for ab initio calculations of correlated materials** -------------------------------------------------------------------------- DFTTools is an official TRIQS application that provides an interface to DFT packages such as Wien2k and VASP for DFT+DMFT calculation. It allows you to turn band-structure calculations results to inputs for full-fledged DFT+DMFT calculations in a few lines. For publications based on results produced with this application please cite `Comput. Phys. Comm. 204, 200 (2016) `_ *Homepage:* ``_ **dftkit - DFT converters for TRIQS** ------------------------------------- dftkit is an official TRIQS application that provides converters turning the output of various DFT codes into the TRIQS-compatible HDF5 format required for DFT+DMFT calculations. Supported codes include Elk, VASP (with the PLOVasp projection tools), Wien2k (with the ``dmftproj`` executable), Quantum Espresso, Wannier90 and generic tight-binding Hamiltonians. It provides a modern, modular successor to the converters historically shipped with DFTTools. *Homepage:* ``_ **modest - Modular Electronic Structure Toolkit** ------------------------------------------------- modest is an official TRIQS application written in C++ with a Python interface that extends the modular design of TRIQS with an API tailored to electronic-structure developers and users. Key features include interfaces to external DFT codes (VASP, Quantum Espresso, Wien2k, Elk, AbInit, Wannier90), a generic representation of DFT one-body data, a flexible description of generic DMFT embedding scenarios, and high-performance implementations of key routines such as the local Green's function, the chemical-potential search and the lattice density. *Homepage:* ``_ **solid_dmft - Python wrapper to perform DFT+DMFT calculations using TRIQS** ---------------------------------------------------------------------------- solid_dmft allows to perform DFT+DMFT ''one-shot'' and charge self-consistent (CSC) calculations from h5 archives, created by DFTTools or VASP/Quantum Espresso input files for multiband systems. It takes advantage of various impurity solvers available in TRIQS. Postprocessing scripts are available to perform analytic continuation and calculate spectral functions. *Homepage:* ``_ **MagInt - ab initio inter-site exchange in correlated insulators** ------------------------------------------------------------------- MagInt is an external TRIQS application for calculating inter-site exchange interactions in correlated insulators. It uses a force-theorem approach based on the Hubbard-I approximation to electronic self-energy. MagInt is applied as a postprocessing tool on top of converged DFT+Hubbard-I calculations. It uses DFTTools and its own implementation of Hubbard-I. MagInt includes interfaces to Wien2k and VASP (experimental). *Homepage* ``_ .. _analytic_continuation: **Analytic Continuation** ========================= **Maxent** ---------- This official TRIQS application provides a modular Maximum Entropy program to perform analytic continuation. *Homepage:* ``_ **Nevanlinna Analytic Continuation** ------------------------------------ This is a TRIQS based implementation of analytical continuation methods using Nevanlinna [#nevanlinna]_ and Caratheodory [#caratheodory]_ functions. The application is written and maintained by S. Iskakov, N. Wentzell and A. Hampel. For papers discussing implemented methods see: .. [#nevanlinna] Jiani Fei, Chia-Nan Yeh, and Emanuel Gull, Phys. Rev. Lett. 126, 056402 (2021) .. [#caratheodory] Jiani Fei, Chia-Nan Yeh, Dominika Zgid, and Emanuel Gull, Phys. Rev. B 104, 165111 (2021) *Homepage:* ``_ **SOM - Stochastic Optimization Method for Analytic Continuation (external)** ----------------------------------------------------------------------------- This external TRIQS application is an optimized implementation of an analytic continuation method proposed by Andrey S. Mishchenko. A detailed description of the method can be found `here `_. It also supports the Stochastic Optimization with Consistent Constraints extensions proposed by Olga Goulko et al in `Phys. Rev. B 95, 014102 (2017) `_. For publications based on results produced with this application please cite `Comput. Phys. Commun. 239, 166 (2019) `_ *Homepage:* ``_ **Interface to Omegamaxent** ---------------------------- This application provides an interface to the `OmegaMaxent `_ Maximum Entropy code. For publications based on results produced with this application please cite `Phys. Rev. E 94, 023303 (2016) `_ *Homepage:* ``_ .. _other_applications: **Other Applications** ====================== **TPRF - The Two-Particle Response Function tool box** ------------------------------------------------------ The two-particle response function tool box (TPRF) is an official TRIQS application that provides efficient (C++/OpenMP/MPI) implementations of the basic operations for higher order response functions such as inversion, products, the random phase approximation, the Bethe Salpeter equation, etc. For publications based on results produced with this application please cite `10.5281/zenodo.2638058 `_ *Homepage:* ``_ **TRIQS Solver benchmarks** --------------------------- This official TRIQS application provides systematic tests and benchmarks of various impurity solvers for a set of reference impurity models. It uses the Python interface of the TRIQS library as a framework. *Homepage:* ``_ **App4Triqs Application Skeleton** ---------------------------------- This official TRIQS application provides a CMake based skeleton for TRIQS applications. Most of the official TRIQS applications are continuously following this project structure. It can be easily adapted for your own application. *Homepage:* ``_