Metadata-Version: 2.1
Name: sparse-ir
Version: 1.0.0
Summary: intermediate representation (IR) basis for electronic propagator
Home-page: https://github.com/SpM-lab/sparse-ir
Author: ['Markus Wallerberger', 'Hiroshi Shinaoka', 'Kazuyoshi Yoshimi', 'Junya Otsuki', 'Chikano Naoya']
Author-email: markus.wallerberger@tuwien.ac.at
License: UNKNOWN
Description: sparse-ir - A library for the intermediate representation of propagators
        ========================================================================
        This library provides routines for constructing and working with the
        intermediate representation of correlation functions.  It provides:
        
         - on-the-fly computation of basis functions for arbitrary cutoff Λ
         - basis functions and singular values are accurate to full precision
         - routines for sparse sampling
        
        
        Installation
        ------------
        Install via `pip <https://pypi.org/project/sparse-ir>`_::
        
            pip install sparse-ir[xprec]
        
        The above line is the recommended way to install `sparse-ir`.  It automatically
        installs the `xprec <https://github.com/tuwien-cms/xprec>`_ package, which
        allows one to compute the IR basis functions with greater accuracy.  If you do
        not want to do this, simply remove the string ``[xprec]`` from the above command.
        
        Install via `conda <https://anaconda.org/spm-lab/sparse-ir>`_::
        
            conda install -c spm-lab sparse-ir xprec
        
        Other than the optional xprec dependency, sparse-ir requires only
        `numpy <https://numpy.org/>`_ and `scipy <https://scipy.org/>`_.
        
        To manually install the current development version, you can use the following::
        
           # Only recommended for developers - no automatic updates!
           git clone https://github.com/SpM-lab/sparse-ir
           pip install -e sparse-ir/[xprec]
        
        Documentation and tutorial
        --------------------------
        Check out our `comprehensive tutorial`_, where we self-contained
        notebooks for several many-body methods - GF(2), GW, Eliashberg equations,
        Lichtenstein formula, FLEX, ... - are presented.
        
        Refer to the `API documentation`_ for more details on how to work
        with the python library.
        
        There is also a `Julia library`_ and (currently somewhat restricted)
        `Fortran library`_ available for the IR basis and sparse sampling.
        
        .. _comprehensive tutorial: https://spm-lab.github.io/sparse-ir-tutorial
        .. _API documentation: https://sparse-ir.readthedocs.io
        .. _Julia library: https://github.com/SpM-lab/SparseIR.jl
        .. _Fortran library: https://github.com/SpM-lab/sparse-ir-fortran
        
        Getting started
        ---------------
        Here is a full second-order perturbation theory solver (GF(2)) in a few
        lines of Python code::
        
            # Construct the IR basis and sparse sampling for fermionic propagators
            import sparse_ir, numpy as np
            basis = sparse_ir.FiniteTempBasis('F', beta=10, wmax=8, eps=1e-6)
            stau = sparse_ir.TauSampling(basis)
            siw = sparse_ir.MatsubaraSampling(basis, positive_only=True)
        
            # Solve the single impurity Anderson model coupled to a bath with a
            # semicircular states with unit half bandwidth.
            U = 1.2
            def rho0w(w):
                return np.sqrt(1-w.clip(-1,1)**2) * 2/np.pi
        
            # Compute the IR basis coefficients for the non-interacting propagator
            rho0l = basis.v.overlap(rho0w)
            G0l = -basis.s * rho0l
        
            # Self-consistency loop: alternate between second-order expression for the
            # self-energy and the Dyson equation until convergence.
            Gl = G0l
            Gl_prev = 0
            while np.linalg.norm(Gl - Gl_prev) > 1e-6:
                Gl_prev = Gl
                Gtau = stau.evaluate(Gl)
                Sigmatau = U**2 * Gtau**3
                Sigmal = stau.fit(Sigmatau)
                Sigmaiw = siw.evaluate(Sigmal)
                G0iw = siw.evaluate(G0l)
                Giw = 1/(1/G0iw - Sigmaiw)
                Gl = siw.fit(Giw)
        
        You may want to start with reading up on the `intermediate representation`_.
        It is tied to the analytic continuation of bosonic/fermionic spectral
        functions from (real) frequencies to imaginary time, a transformation mediated
        by a kernel ``K``.  The kernel depends on a cutoff, which you should choose to
        be ``lambda_ >= beta * W``, where ``beta`` is the inverse temperature and ``W``
        is the bandwidth.
        
        One can now perform a `singular value expansion`_ on this kernel, which
        generates two sets of orthonormal basis functions, one set ``v[l](w)`` for
        real frequency side ``w``, and one set ``u[l](tau)`` for the same obejct in
        imaginary (Euclidean) time ``tau``, together with a "coupling" strength
        ``s[l]`` between the two sides.
        
        By this construction, the imaginary time basis can be shown to be *optimal* in
        terms of compactness.
        
        .. _intermediate representation: https://arxiv.org/abs/2106.12685
        .. _singular value expansion: https://w.wiki/3poQ
        
        License and citation
        --------------------
        This software is released under the MIT License.  See LICENSE.txt for details.
        
        If you find the intermediate representation, sparse sampling, or this software
        useful in your research, please consider citing the following papers:
        
         - Hiroshi Shinaoka et al., `Phys. Rev. B 96, 035147`_  (2017)
         - Jia Li et al., `Phys. Rev. B 101, 035144`_ (2020)
         - Markus Wallerberger et al., `arXiv 2206.11762`_ (2022)
        
        If you are discussing sparse sampling in your research specifically, please
        also consider citing an independently discovered, closely related approach, the
        MINIMAX isometry method (Merzuk Kaltak and Georg Kresse,
        `Phys. Rev. B 101, 205145`_, 2020).
        
        .. _Phys. Rev. B 96, 035147: https://doi.org/10.1103/PhysRevB.96.035147
        .. _Phys. Rev. B 101, 035144: https://doi.org/10.1103/PhysRevB.101.035144
        .. _arXiv 2206.11762: https://doi.org/10.48550/arXiv.2206.11762
        .. _Phys. Rev. B 101, 205145: https://doi.org/10.1103/PhysRevB.101.205145
        
Keywords: irbasis many-body propagator svd
Platform: UNKNOWN
Classifier: Development Status :: 5 - Production/Stable
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Scientific/Engineering :: Physics
Classifier: License :: OSI Approved :: MIT License
Classifier: Programming Language :: Python :: 3
Requires-Python: >=3
Description-Content-Type: text/x-rst
Provides-Extra: doc
Provides-Extra: test
Provides-Extra: xprec
