Logo
  • Welcome
    • TRIQS Community
    • Where to start?
  • TRIQS Software Stack
    • Core libraries
    • The TRIQS library
    • Numerical Algorithms
    • Applications
      • Applications based on TRIQS
        • Impurity Solvers
          • Hybridization-expansion solver
          • Segment Picture Hybridization-expansion solver
          • Interaction-expansion solver
          • X-Crossing Approximation (XCA) solver
          • Hubbard I solver
          • Hartree Fock solver
          • gem - Gutzwiller Embedding Method
          • PYED - Exact diagonalization for finite quantum systems (external)
          • Interface to the pomerol exact diagonalization solver (external)
          • Interface to the EDIpack impurity solver
          • Interface to the w2dynamics impurity solver
          • Interface to the NRG Ljubljana impurity solver
        • Ab-Initio Tools
          • DFT tools - Toolbox for ab initio calculations of correlated materials
          • dftkit - DFT converters for TRIQS
          • modest - Modular Electronic Structure Toolkit
          • solid_dmft - Python wrapper to perform DFT+DMFT calculations using TRIQS
          • MagInt - ab initio inter-site exchange in correlated insulators
        • Analytic Continuation
          • Maxent
          • Nevanlinna Analytic Continuation
          • SOM - Stochastic Optimization Method for Analytic Continuation (external)
          • Interface to Omegamaxent
        • Other Applications
          • TPRF - The Two-Particle Response Function tool box
          • TRIQS Solver benchmarks
          • App4Triqs Application Skeleton
  • Installation
    • Packaged Versions of TRIQS
      • Ubuntu Debian packages
      • Anaconda
      • Docker
      • Apptainer
      • Binder
    • Compiling TRIQS from source using EasyBuild
    • Compiling TRIQS from source (Advanced)
      • Prerequisites
        • A complete list of requirements
          • C++ compilers
          • Tools and Libraries
          • Building the TRIQS documentation
        • Installing required libraries on Ubuntu
          • Issues
        • Prerequisites for the TRIQS Compilation on Mac OS X
          • Disclaimer
          • Installation of the dependencies
      • Installation steps
        • Using the command line
        • Using the provided Python script
      • Environment setup
      • Further reading
        • Customizing your installation
          • cmake options
        • Unix environment variables
          • Common environment variables
          • Environment variables for software developement
          • Environment variables affecting OpenMP
        • Python Virtual Environments
          • Usage
          • Compiling a package from source
        • Using the clang compiler
          • Get and install clang on linux
          • Usage
          • libclang
        • Version compatibility
          • TRIQS version numbering
          • TRIQS applications version numbering
          • How to determine the version of the installed TRIQS library
  • API Documentation
    • C++ API
    • Python API
      • triqs.atom_diag
        • Examples
        • triqs.atom_diag.AtomDiag
          • AtomDiag()
        • triqs.atom_diag.atom_diag
          • triqs.atom_diag.atom_diag.act
          • triqs.atom_diag.atom_diag.atomic_density_matrix
          • triqs.atom_diag.atom_diag.atomic_g_iw
          • triqs.atom_diag.atom_diag.atomic_g_l
          • triqs.atom_diag.atom_diag.atomic_g_tau
          • triqs.atom_diag.atom_diag.atomic_g_w
          • triqs.atom_diag.atom_diag.partition_function
          • triqs.atom_diag.atom_diag.quantum_number_eigenvalues
          • triqs.atom_diag.atom_diag.quantum_number_eigenvalues_checked
          • triqs.atom_diag.atom_diag.trace_rho_op
          • triqs.atom_diag.atom_diag.AtomDiagComplex
          • triqs.atom_diag.atom_diag.AtomDiagReal
      • triqs.dos
        • triqs.dos.dos
          • triqs.dos.dos.dos_from_file
          • triqs.dos.dos.DOS
          • triqs.dos.dos.DOSFromFunction
        • triqs.dos.hilbert_transform
          • triqs.dos.hilbert_transform.HilbertTransform
      • triqs.experimental
        • triqs.experimental.lattice
          • triqs.experimental.lattice.lattice
        • triqs.experimental.utility
          • triqs.experimental.utility.utility
      • triqs.fit
        • triqs.fit.fit
          • triqs.fit.fit.linear
          • triqs.fit.fit.quadratic
          • triqs.fit.fit.Fit
      • triqs.gfs
        • triqs.gfs.backwd_compat
          • triqs.gfs.backwd_compat.gf_imfreq
          • triqs.gfs.backwd_compat.gf_imtime
          • triqs.gfs.backwd_compat.gf_legendre
          • triqs.gfs.backwd_compat.gf_refreq
          • triqs.gfs.backwd_compat.gf_retime
        • triqs.gfs.block2_gf
          • triqs.gfs.block2_gf.Block2Gf
        • triqs.gfs.block_gf
          • triqs.gfs.block_gf.call_factory_from_dict
          • triqs.gfs.block_gf.fix_gf_struct_type
          • triqs.gfs.block_gf.BlockGf
        • triqs.gfs.descriptor_base
          • triqs.gfs.descriptor_base.convert_scalar_to_const
          • triqs.gfs.descriptor_base.is_lazy
          • triqs.gfs.descriptor_base.is_scalar
          • triqs.gfs.descriptor_base.Omega
          • triqs.gfs.descriptor_base.iOmega_n
          • triqs.gfs.descriptor_base.Base
          • triqs.gfs.descriptor_base.BaseBlock
          • triqs.gfs.descriptor_base.Const
          • triqs.gfs.descriptor_base.Function
          • triqs.gfs.descriptor_base.LazyCTX
          • triqs.gfs.descriptor_base.Omega_
        • triqs.gfs.descriptors
          • triqs.gfs.descriptors.semi
          • triqs.gfs.descriptors.Flat
          • triqs.gfs.descriptors.Fourier
          • triqs.gfs.descriptors.LegendreToMatsubara
          • triqs.gfs.descriptors.MatsubaraToLegendre
          • triqs.gfs.descriptors.OneFermionInTime
          • triqs.gfs.descriptors.SemiCircular
          • triqs.gfs.descriptors.Wilson
        • triqs.gfs.dlr_crm_dyson_solver
          • triqs.gfs.dlr_crm_dyson_solver.minimize_dyson
        • triqs.gfs.gf
          • triqs.gfs.gf.add_method_helper
          • triqs.gfs.gf.bckwd
          • triqs.gfs.gf.call_factory_from_dict
          • triqs.gfs.gf.AddMethod
          • triqs.gfs.gf.CallProxyNone
          • triqs.gfs.gf.Gf
          • triqs.gfs.gf.Idx
        • triqs.gfs.gf_factories
          • triqs.gfs.gf_factories.gf_factories_dlr_imfreq
          • triqs.gfs.gf_factories.gf_factories_dlr_imtime
          • triqs.gfs.gf_factories.gf_factories_fourier
          • triqs.gfs.gf_factories.gf_factories_hermitian
        • triqs.gfs.gf_fnt
          • triqs.gfs.gf_fnt.gf_fnt_fit_and_density
          • triqs.gfs.gf_fnt.gf_fnt_fourier
          • triqs.gfs.gf_fnt.gf_fnt_misc
        • triqs.gfs.lazy_expressions
          • triqs.gfs.lazy_expressions.all_terminals
          • triqs.gfs.lazy_expressions.eval_expr
          • triqs.gfs.lazy_expressions.eval_expr_with_context
          • triqs.gfs.lazy_expressions.lazy_function
          • triqs.gfs.lazy_expressions.make_lazy
          • triqs.gfs.lazy_expressions.transform
          • triqs.gfs.lazy_expressions.LazyExpr
          • triqs.gfs.lazy_expressions.LazyExprTerminal
        • triqs.gfs.plot
          • triqs.gfs.plot.dispatcher
          • triqs.gfs.plot.bz
          • triqs.gfs.plot.bz_x_x
          • triqs.gfs.plot.one_var
          • triqs.gfs.plot.plot_base
          • triqs.gfs.plot.select_indices
        • triqs.gfs.semicirc
          • Functions
          • triqs.gfs.semicirc.g_semicirc_tau
          • triqs.gfs.semicirc.g_semicirc_tau_adapquad
          • triqs.gfs.semicirc.g_semicirc_w
          • triqs.gfs.semicirc.g_semicirc_z
        • triqs.gfs.tools
          • triqs.gfs.tools.conjugate
          • triqs.gfs.tools.delta
          • triqs.gfs.tools.discretize_bath
          • triqs.gfs.tools.dyson
          • triqs.gfs.tools.fit_legendre
          • triqs.gfs.tools.inverse
          • triqs.gfs.tools.make_delta
          • triqs.gfs.tools.make_zero_tail
          • triqs.gfs.tools.map_block
          • triqs.gfs.tools.read_gf_from_txt
          • triqs.gfs.tools.transpose
          • triqs.gfs.tools.write_gf_to_txt
        • triqs.gfs.wrapped_aux
          • triqs.gfs.wrapped_aux.wrapped_aux_other
          • triqs.gfs.wrapped_aux.wrapped_aux_target_rank_0
          • triqs.gfs.wrapped_aux.wrapped_aux_target_rank_1
          • triqs.gfs.wrapped_aux.wrapped_aux_target_rank_2
          • triqs.gfs.wrapped_aux.wrapped_aux_target_rank_3
          • triqs.gfs.wrapped_aux.wrapped_aux_target_rank_4
      • triqs.lattice
        • triqs.lattice.bz_patch
          • triqs.lattice.bz_patch.BZPatch
        • triqs.lattice.lattice_tools
          • triqs.lattice.lattice_tools.dos
          • triqs.lattice.lattice_tools.dos_patch
          • triqs.lattice.lattice_tools.BravaisLattice
          • triqs.lattice.lattice_tools.BrillouinZone
          • triqs.lattice.lattice_tools.TightBinding
        • triqs.lattice.point
          • triqs.lattice.point.LatticePoint
        • triqs.lattice.super_lattice
          • triqs.lattice.super_lattice.TBSuperLattice
        • triqs.lattice.tight_binding
          • triqs.lattice.tight_binding.dos
          • triqs.lattice.tight_binding.dos_patch
          • triqs.lattice.tight_binding.TBLattice
        • triqs.lattice.utils
          • triqs.lattice.utils.TB_from_pythTB
          • triqs.lattice.utils.TB_from_wannier90
          • triqs.lattice.utils.TB_to_sympy
          • triqs.lattice.utils.extend_wannier90_to_spin
          • triqs.lattice.utils.k_space_path
          • triqs.lattice.utils.parse_hopping_from_wannier90_hr_dat
          • triqs.lattice.utils.parse_lattice_vectors_from_wannier90_wout
      • triqs.mc_tools
        • triqs.mc_tools.random_generator
          • triqs.mc_tools.random_generator.random_generator_names
          • triqs.mc_tools.random_generator.random_generator_names_list
          • triqs.mc_tools.random_generator.RandomGenerator
      • triqs.mesh
        • triqs.mesh.matsubara_freq
          • triqs.mesh.matsubara_freq.MatsubaraFreq
        • triqs.mesh.mesh_point
          • triqs.mesh.mesh_point.MeshPoint
          • triqs.mesh.mesh_point.MeshValueGenerator
        • triqs.mesh.mesh_product
          • triqs.mesh.mesh_product.call_factory_from_dict
          • triqs.mesh.mesh_product.MeshProduct
        • triqs.mesh.meshes
          • triqs.mesh.meshes.make_adjoint_mesh
          • triqs.mesh.meshes.EnergyT
          • triqs.mesh.meshes.MeshBrZone
          • triqs.mesh.meshes.MeshChebyshev
          • triqs.mesh.meshes.MeshCycLat
          • triqs.mesh.meshes.MeshDLR
          • triqs.mesh.meshes.MeshDLRImFreq
          • triqs.mesh.meshes.MeshDLRImTime
          • triqs.mesh.meshes.MeshImFreq
          • triqs.mesh.meshes.MeshImTime
          • triqs.mesh.meshes.MeshLegendre
          • triqs.mesh.meshes.MeshReFreq
          • triqs.mesh.meshes.MeshReFreqLog
          • triqs.mesh.meshes.MeshReFreqPts
          • triqs.mesh.meshes.MeshReTime
      • triqs.operators
        • Examples
        • triqs.operators.operators
          • triqs.operators.operators.c
          • triqs.operators.operators.c_dag
          • triqs.operators.operators.dagger
          • triqs.operators.operators.is_op_hermitian
          • triqs.operators.operators.n
          • triqs.operators.operators.CanonicalOpsT
          • triqs.operators.operators.Operator
        • triqs.operators.util
          • triqs.operators.util.U_matrix
          • triqs.operators.util.extractors
          • triqs.operators.util.hamiltonians
          • triqs.operators.util.observables
          • triqs.operators.util.op_struct
      • triqs.plot
        • triqs.plot.mpl_interface
          • triqs.plot.mpl_interface.oplot
          • triqs.plot.mpl_interface.oploti
          • triqs.plot.mpl_interface.oplotr
          • triqs.plot.mpl_interface.use_amsmath
        • triqs.plot.protocol
          • triqs.plot.protocol.clip_array
          • triqs.plot.protocol.plot_protocol_apply
          • triqs.plot.protocol.plot_function_table
      • triqs.stat
        • triqs.stat.histogram
          • triqs.stat.histogram.plot
        • triqs.stat.histograms
          • triqs.stat.histograms.cdf
          • triqs.stat.histograms.pdf
          • triqs.stat.histograms.Histogram
      • triqs.sumk
        • triqs.sumk.sumk_discrete
          • triqs.sumk.sumk_discrete.SumkDiscrete
        • triqs.sumk.sumk_discrete_from_lattice
          • triqs.sumk.sumk_discrete_from_lattice.SumkDiscreteFromLattice
      • triqs.utility
        • triqs.utility.bound_and_bisect
          • triqs.utility.bound_and_bisect.bound_and_bisect
          • triqs.utility.bound_and_bisect.determine_bounds
        • triqs.utility.capture_stdout
        • triqs.utility.comparison_tests
          • triqs.utility.comparison_tests.assert_array_close_to_scalar
          • triqs.utility.comparison_tests.assert_arrays_are_close
          • triqs.utility.comparison_tests.assert_block2_gfs_are_close
          • triqs.utility.comparison_tests.assert_block_gfs_are_close
          • triqs.utility.comparison_tests.assert_gfs_are_close
        • triqs.utility.dichotomy
          • triqs.utility.dichotomy.dichotomy
        • triqs.utility.dist_on_nodes
          • triqs.utility.dist_on_nodes.DistributionOnNodes
          • triqs.utility.dist_on_nodes.DistributionOnNodesOneStack
          • triqs.utility.dist_on_nodes.DistributionOnNodesTest
        • triqs.utility.h5diff
          • Attributes
          • triqs.utility.h5diff.compare
          • triqs.utility.h5diff.h5diff
        • triqs.utility.mpi
          • triqs.utility.mpi.check_for_mpi
        • triqs.utility.mpi_mpi4py
          • Attributes
          • triqs.utility.mpi_mpi4py.all_reduce
          • triqs.utility.mpi_mpi4py.barrier
          • triqs.utility.mpi_mpi4py.bcast
          • triqs.utility.mpi_mpi4py.is_master_node
          • triqs.utility.mpi_mpi4py.master_gets_host_names
          • triqs.utility.mpi_mpi4py.myprint_err
          • triqs.utility.mpi_mpi4py.myprint_out
          • triqs.utility.mpi_mpi4py.recv
          • triqs.utility.mpi_mpi4py.report
          • triqs.utility.mpi_mpi4py.send
          • triqs.utility.mpi_mpi4py.slice_array
          • triqs.utility.mpi_mpi4py.slice_inf
          • triqs.utility.mpi_mpi4py.slice_sup
        • triqs.utility.mpi_nompi
          • Attributes
          • triqs.utility.mpi_nompi.all_reduce
          • triqs.utility.mpi_nompi.barrier
          • triqs.utility.mpi_nompi.bcast
          • triqs.utility.mpi_nompi.is_master_node
          • triqs.utility.mpi_nompi.master_gets_host_names
          • triqs.utility.mpi_nompi.myprint_err
          • triqs.utility.mpi_nompi.myprint_out
          • triqs.utility.mpi_nompi.recv
          • triqs.utility.mpi_nompi.report
          • triqs.utility.mpi_nompi.send
          • triqs.utility.mpi_nompi.slice_array
        • triqs.utility.redirect
          • Attributes
          • triqs.utility.redirect.start_redirect
          • triqs.utility.redirect.stop_redirect
          • triqs.utility.redirect.T
        • triqs.utility.utilities
          • triqs.utility.utilities.TimePt
  • User guide
    • Why use TRIQS?
      • Dynamical mean-field theory on a Bethe lattice
    • Python Tutorials
      • Basics
        • Introducing Python and the IPython Notebook
          • Script mode
          • Interactive shell mode
          • The IPython Notebook
        • A Very Short Introduction to Python
          • Calculating
          • Simple loops / indentation
          • If statements
          • Defining a function
          • Importing modules
          • Lists
          • The NumPy Library
          • Defining a new class
          • Getting help
        • Matplotlib Examples
          • Goal of this tutorial
          • Inline plots
          • Making the plot prettier
          • Subplots
          • Histograms and text
          • Python-like approach to matplotlib
          • More examples
        • TRIQS Green’s functions
          • Matrix-Valued Green’s functions
          • Block Green’s functions
          • Additional Initialization Descriptors
          • Imaginary-frequency Green’s functions
          • Arithmetic Operations
          • Obtaining the density
          • Fourier transforms
          • Compact meshes for imaginary time / frequency: DLR Green’s function
          • Pade analytical continuation
          • Exercises
        • HDF5 Archives
        • Writing to an archive
          • Reading from an archive
        • Manipulating fermionic operators
          • Fundamental operators
          • Number operator
          • Operations with operators
          • Exact Diagonalization
        • Introduction to multivariable Green’s functions
          • Imports and parameters
          • Constructing and Initializing a Lattice Green’s function
          • NumPy Broadcasting
          • Evaluate the Green’s function
          • Partial evaluation
          • Defining a Tight-Binding Hamiltonian
      • Model DMFT
        • A first DMFT calculation
          • The iterated perturbation theory
          • Dynamical mean-field theory
          • Bethe lattice DMFT
          • Visualizing the Mott transition
          • Comparison with the literature
        • General reminder: Anderson impurity model and CTHYB solver
        • The TRIQS/CTHYB impurity solver
          • Setting up the impurity solver
          • Visualizing the imaginary time sampled \(G(\tau)\)
          • Visualizing the Matsubara-frequency results
        • Single-orbital Hubbard model
          • Solution 1
          • Solution 2
          • Solution 3
          • Solution 4
          • Solution 5
          • Solution 6
        • Two-orbital Hubbard model
          • Solution 1
          • Solution 2
          • Solution of exercise 3
        • Valence-Bond DMFT solution of the Hubbard model
          • Analyzing the precomputed results
      • Two-particle Response
        • Fermions on the square lattice & perfect nesting
          • Square lattice with nearest-neighbour hopping
          • Non-interacting lattice Green’s function
          • Fermi surface nesting
        • Susceptibility \(\chi_0\) of non-interacting fermions
          • Theory
          • Fast calculation using Fourier transform
          • Goals and questions
          • Compute the susceptibility \(\chi_0(\mathbf{q}, i\omega_n)\)
          • Static susceptibility \(\chi_0(\mathbf{q}, \omega=0)\) and perfect nesting
        • The random phase approximation (RPA)
          • RPA solver
        • Two-particle self consistency (TPSC)
          • Theory
          • Behaviour of \(U_{sp}\) and \(U_{ch}\) vs. \(U\)
        • Finite temperature antiferromagnetism in two dimensional systems
          • Mermin-Wagner theorem
          • TPSC and the Mermin-Wagner theorem
          • Code from previous notebooks
          • \(\chi_0\) calculator for arbitrary \(\beta\)
          • RPA spin structure factor \(S_{RPA}\) as a function of temperature \(T\)
          • TPSC spin structure factor \(S_{TPSC}\) as a function of temperature
          • Questions
          • Remarks
      • A tight-binding model on a square lattice
      • Learn more about Python, ipython and the notebook
  • Changelog
    • Version 4.0.0
      • Python bindings: cpp2py to clair + c2py
      • Renamings
      • Removal of deprecated API
      • Experimental package
      • Documentation
      • Dependency Management
      • General
      • gfs
      • mesh
      • det_manip
      • mc_generic
      • mc_tools
      • stat
      • operators
      • lattice
      • blockgf
      • py
      • plot
      • cmake
      • porting_tools
      • packaging
      • doc
      • jenkins
    • Version 3.3.3
      • General
      • blockgf
      • mc_generic
      • cmake
      • doc
      • jenkins
      • test
    • Version 3.3.2
      • General
      • Gf
      • doc
      • cmake
    • Version 3.3.1
      • General
      • doc
    • Version 3.3.0
      • General
      • Gf
      • atom_diag
      • doc
      • cmake
      • jenkins
    • Version 3.2.1
      • General
      • doc
      • jenkins
      • cmake
    • Version 3.2.0
      • Porting Script
      • API Changes
      • General
      • Gf
      • Meshes
      • DLR
      • Lattice
      • det_manip
      • mc_generic
      • MPI
      • Fixes
      • doc
      • cmake
      • jenkins
    • Version 3.1.1
      • cmake
      • doc
      • gf
      • Meshes
    • Version 3.1.0
      • Porting Script
      • Deprecate use of string indices for Green functions
      • Change in gf_struct objects
      • Green function meshes (C++)
      • Move multi-array into TRIQS/nda library
      • triqs::stat Rework
      • Bath discretization function
      • Jenkins Sanitizer Checks
      • New website theme
      • TightBinding and TBLattice improvements
      • Require C++20 capable compiler
      • General
      • atom_diag
      • cmake
      • cpp2py
      • doc
      • gf
      • jenkins
      • lattice
      • mc_generic
      • mesh
      • mpi
      • nda
    • Version 3.0.2
      • atom_diag
      • gf
      • cmake
      • Python 3.10
      • c++20
    • Version 3.0.1
      • Issue 819 - Atom Diag
      • General
      • array
      • Gf
      • cmake
      • jenkins
      • doc
    • Version 3.0.0
      • Renamings
      • Dependency Management
      • h5py dependency
      • Removal of deprecated API
      • General
      • atom_diag
      • cmake
      • detmanip
      • doc
      • gf
      • jenkins
      • operators
      • packaging
    • Version 2.2.3
      • General
      • cmake
      • cpp2py
      • gf
      • jenkins
    • Version 2.2.2
      • doc
      • gf
      • cmake
      • General
    • Version 2.2.1
      • doc
      • cmake
      • General
    • Version 2.2.0
      • Make range and itertools functionality standalone
      • Make mpi functionality standalone and change namespace
      • Non-owning views (C++)
      • Dynamic Analyzer Checks (ASAN, UBSAN)
      • No longer install googletest
      • app4triqs
      • arrays
      • cmake
      • doc
      • fourier
      • gf
      • h5
      • itertools
      • jenkins
      • mc_generic
      • mpi
      • lattice
      • operators
      • packaging
      • pytriqs
      • General
    • Version 2.1.1
      • jenkins
      • doc
      • cmake
      • General
    • Version 2.1.0
      • gf
      • array
      • clef
      • BlockGf
      • cmake
      • lapack
      • lattice
      • tail
      • det_manip
      • atom_diag
      • mc_tools
      • doc
      • General
      • pytriqs
      • fourier
    • Version 2.0.0
      • fourier,tail
      • cmake
      • hdf5
      • arrays
      • doc
      • gf/py
      • py
      • General
      • travis
      • gf
      • tail
      • pytriqs
      • pytriqs/gf
      • test
      • tail,fourier
    • Version 1.5
      • API changes
    • Version 1.4
      • Documentation
      • Installation
      • Many-body operators
      • Green’s functions
      • Tests
    • Version 1.3
      • Installation
      • Green functions
      • Many-body operators
      • Monte-Carlo tools
      • Determinant manipulation
      • HDF5
      • c++2py
      • Tests
      • Miscellaneous
    • Version 1.2
      • C++
      • Python
      • Green Functions
      • Version 1.1
      • Version 1.0
      • Python classes
      • Archives
  • About TRIQS
    • Authors & contributors
    • Citation
    • License
    • Disclaimer
    • Logo files
    • More
      • Contributing
        • Issues and feature requests
        • Contributing to code and documentation
          • How to make a pull request?
          • How to contribute to documentation?
        • Github discussions
      • Frequently-asked questions
        • Q: How do I write my GF data to text files, e.g. to plot using other plotting tools?
        • Q: How do I save the triqs hash and script for debugging purposes?
TRIQS
  • Table of contents
  • View page source

Table of contents

  • Welcome
    • TRIQS Community
    • Where to start?
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