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<89919391+editorialbot@users.noreply.github.com> Date: Sun, 1 Oct 2023 21:29:17 +0100 Subject: [PATCH 2/3] Creating 10.21105.joss.05115.crossref.xml --- joss.05115/10.21105.joss.05115.crossref.xml | 490 ++++++++++++++++++++ 1 file changed, 490 insertions(+) create mode 100644 joss.05115/10.21105.joss.05115.crossref.xml diff --git a/joss.05115/10.21105.joss.05115.crossref.xml b/joss.05115/10.21105.joss.05115.crossref.xml new file mode 100644 index 0000000000..bfe4cb6ae1 --- /dev/null +++ b/joss.05115/10.21105.joss.05115.crossref.xml @@ -0,0 +1,490 @@ + + + + 20231001T202853-45d2baac778e64c54565454a2b2a3f42c0ebf3b3 + 20231001202853 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 10 + 2023 + + + 8 + + 90 + + + + The Generalized Green’s function Cluster Expansion: A +Python package for simulating polarons + + + + Matthew R. + Carbone + 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IEEE Transactions on Parallel and Distributed +Systems, 33(4), 842–853. +https://doi.org/10.1109/TPDS.2021.3084070 + + + + + + From b05bb6fb50a04dcc9e4f510312e181e57d44a6b8 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Sun, 1 Oct 2023 21:29:17 +0100 Subject: [PATCH 3/3] Creating 10.21105.joss.05115.jats --- joss.05115/10.21105.joss.05115.jats | 954 ++++++++++++++++++++++++++++ 1 file changed, 954 insertions(+) create mode 100644 joss.05115/10.21105.joss.05115.jats diff --git a/joss.05115/10.21105.joss.05115.jats b/joss.05115/10.21105.joss.05115.jats new file mode 100644 index 0000000000..70b58a587e --- /dev/null +++ b/joss.05115/10.21105.joss.05115.jats @@ -0,0 +1,954 @@ + + +

+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +5115 +10.21105/joss.05115 + +The Generalized Green’s function Cluster Expansion: A +Python package for simulating polarons + + + +https://orcid.org/0000-0002-5181-9513 + +Carbone +Matthew R. + +mcarbone@bnl.gov + +* + + +https://orcid.org/0000-0002-1622-9382 + +Fomichev +Stepan + + + + + +https://orcid.org/0000-0001-9413-6344 + +Millis +Andrew J. + + + + + +https://orcid.org/0000-0002-6736-1893 + +Berciu +Mona + + + + + +https://orcid.org/0000-0002-5265-5637 + +Reichman +David R. + + + + +https://orcid.org/0000-0002-9994-5789 + +Sous +John + + + +* + + + +Computational Science Initiative, Brookhaven National +Laboratory, Upton, New York 11973, USA + + + + +Department of Physics and Astronomy, University of British +Columbia, Vancouver, British Columbia V6T 1Z1, Canada + + + + +Stewart Blusson Quantum Matter Institute, University of +British Columbia, Vancouver, British Columbia, V6T 1Z4 +Canada + + + + +Department of Physics, Columbia University, New York, New +York 10027, USA + + + + +Center for Computational Quantum Physics, Flatiron +Institute, New York, New York 10010, USA + + + + +Department of Chemistry, Columbia University, New York, New +York 10027, USA + + + + +Department of Physics, Stanford University, Stanford, +California 93405, USA + + + + +Geballe Laboratory for Advanced Materials, Stanford +University, Stanford, California 94305, USA + + + + +* E-mail: mcarbone@bnl.gov +* E-mail: + +8 +90 +5115 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Python +computational quantum physics +condensed matter physics +materials science + + + + + + Summary +

We present an efficient implementation of the Generalized Green’s + function Cluster Expansion (GGCE), which is a new method for computing + the ground-state properties and dynamics of polarons (single electrons + coupled to lattice vibrations) in model electron-phonon systems. The + GGCE works at arbitrary temperature and is well suited for a variety + of electron-phonon couplings, including, but not limited to, site and + bond Holstein and Peierls (Su-Schrieffer-Heeger) couplings, and + couplings to multiple phonon modes with different energy scales and + coupling strengths. Quick calculations can be performed efficiently on + a laptop using solvers from NumPy and SciPy, or in parallel at scale + using the PETSc sparse linear solver engine.

+
+ + Statement of need +

The electron-phonon problem is of both fundamental relevance and + practical importance in materials science + (Mahan, + 2010; + Peter + & Cardona, 2010). Electron-phonon interactions promote a + variety of states, low-temperature phases and high-temperature + transport phenomena in quantum materials. For example, they are + essential to the understanding of the behavior of solar cells + (Schilcher + et al., 2021) and semiconductors + (Fratini + et al., 2020). In the dilute-carrier-density limit, + electron-phonon coupling gives rise to quasiparticles called polarons + whose properties encode the physics of materials in various + temperature regimes.

+

Research on polarons has been divided into two thrusts: fundamental + theoretical work focused on qualitative physical aspects + (Mahan, + 2010) and applied research focused on obtaining quantitative + properties relevant to specific materials + (Giustino, + 2017; + Lee + et al., 2018; + Poncé + et al., 2016; + Sio + et al., 2019b, + 2019a; + Zhou + et al., 2021; + Zhou + & Bernardi, 2016). This paper presents a new scientific + software that aims to bridge this gap. It allows for the treatment of + polaron statics and dynamics in models of electron-phonon coupling of + almost arbitrary form provided that they are sufficiently + short-ranged. It presents a self-contained first step in an ongoing + effort to combine an ab initio understanding of + materials and exact many-body analysis of polaron states.

+
+ + Software summary +

The GGCE method is a numerically exact extension + of a family of variational approaches known in the theoretical physics + community as Momentum Average (MA) methods + (Berciu, + 2006; + Glen + L. Goodvin et al., 2006). Details on the theoretical framework + of GGCE can be found in Carbone et al + (Carbone, + Reichman, et al., 2021; + Carbone, + Millis, et al., 2021). Our code, named for the method, is a + Python package meant to make implementing the GGCE framework as + straightforward as possible. In addition, through only slight + modifications to our standard API, the user can invoke powerful PETSc + sparse solvers for massively parallel computations at scale + (Balay + et al., 1997, + 2022a, + 2022b; + Zhang + et al., 2022).

+

A fundamental insight of the MA approximation is to utilize a + variational space formed of clouds of spatially clustered phonon + configurations with the electron allowed to be anywhere in the system. + Through comparison with exact methods, this approximation was shown to + yield quantitatively accurate results. In order to systematically + converge MA to the limit of infinite Hilbert space dimension, the + cloud size and total phonon number, which serve as control parameters, + are taken to infinity + (Glen + L. Goodvin et al., 2006). This, however, requires the + derivation of a set of equations corresponding to a given cloud size + for all cloud sizes smaller than a cutoff. This cutoff is then + increased until convergence is achieved. The ever-increasing + complexity of the structure of the system of equations at large cloud + sizes means that this approach can very quickly become intractable to + do by hand + (Marchand + et al., 2010; + Sous et + al., 2017, + 2018), + especially in the regime of small phonon energies where large cloud + sizes are usually needed in order to converge to the numerically exact + limit. Carbone et al proposed a generalized + implementation of the MA method which automates the generation and + solution of the systems of equations for arbitrary cloud sizes + (Carbone, + Reichman, et al., 2021). Benchmarks of GGCE on several model + systems verified that convergence with cloud size is fast, rendering + this an efficient and controlled numerically exact method even in + challenging parameter regimes.

+

Previous studies using GGCE focused on polarons at zero + temperature. We also include a new functionality which allows the + study of polarons at finite temperature. Here, we make use of the + Thermofield Double formalism + (Suzuki, + 1985; + Takahashi + & Umezawa, 1996), which exactly maps any given model at + finite temperature to one at zero temperature with couplings to real + and fictitious phonons. This model can be solved naturally using the + apparatus of the zero-temperature GGCE method. Benchmarks of this + approach are ongoing, and preliminary results suggest that the method + may be competitive with state-of-the-art methods. A paper with these + results is currently in preparation.

+

Formally, the GGCE functions as an on-the-fly generator of + equations of motion for the single-particle Green’s function given a + set of control parameters (cloud size, total phonon number, and their + extensions to systems with multiple phonon modes) and input model + parameters (energy scales, coupling strength, etc.). The generated + system of equations is then solved numerically in order to obtain the + Green’s function of interest using a chosen solver. Furthermore, the + equation of motion dictates how different Green’s functions or + propagators couple, and so one can use the solver to numerically + obtain any one particular propagator or a set of them, which can be + used to construct other quantities such as the optical conductivity + (Glen + L. Goodvin et al., 2011) or resonant inelastic X-ray scattering + spectrum + (Bieniasz + et al., 2021).

+

The GGCE code consists of three components detailed in our + documentation: models, systems and solvers.

+ + +

Models completely describe the Hamiltonian system to solve, and + the level of theory (specified by the control parameters) at which + to solve it;

+
+ +

Systems construct all of the objects required to build the + matrix to solve the system of equations;

+
+ +

Solvers utilize different back-ends to actually solve the + constructed matrix in an efficient manner.

+
+
+ + Models +

The choice of model completely defines the type of + electron-phonon coupling used in the Hamiltonian. Every model + Hamiltonian implemented so far assumes a lattice with + nearest-neighbor hopping of electrons and Einstein (dispersionless) + phonons. The user can set the electron hopping, phonon frequency and + type and strength of the electron-phonon coupling. Currently, we + have implemented the Holstein, site Peierls (site + Su-Schrieffer-Heeger), bond Peierls (bond Su-Schrieffer-Heeger) and + Edwards Fermion-boson models (as well as any arbitrary combination + of these).

+
+ + Systems +

The Systems objects are a helpful intermediary for performing the + sometimes expensive step of constructing the Python objects required + for building matrices of linear equations. Systems are instantiated + from a Model. At creation, using the information in the Model about + the electron-phonon couplings, Systems automatically construct and + store the equations-of-motion object called the “basis”. The basis + remains “un-evaluated”: it is passed into the Solver, where it can + be used to obtain a matrix of equation coefficients at any values of + momentum and frequency. In this way, the basis is constructed only + once, and then simply called repeatedly to determine the + coefficients. Construction of the basis follows the scheme outlined + in Carbone et al + (Carbone, + Reichman, et al., 2021). For relatively small clouds, the + basis can be visualized for sanity-checking the calculation, using a + method that pretty-prints the equations’ structure.

+

When provided a directory, the System will also automatically + checkpoint the basis to disk using pickle, + allowing for a later restart of a failed computation or for + restarting long jobs on a cluster with time-limited jobs without the + expensive re-computation of the basis.

+
+ + Solvers +

At the heart of GGCE are the Solvers, which implement different + approaches to solving the linear systems of equations obtained by a + System object. The simplest of these uses NumPy’s dense solver, + which solves the equation-of-motion matrix using an efficient + continued fraction approach + (Glen + L. Goodvin et al., 2006), or SciPy’s sparse solver. For truly + large-scale computations with sizable phonon clouds and/or many + different electron-phonon couplings operating simultaneously, GGCE + interfaces with the powerful, massively parallel PETSc sparse solver + engine. All GGCE Solvers are MPI-enabled, and allow for a variety of + parallelization schemes, all of which are detailed in our + documentation. At the extreme, the PETSc interface can parallelize + calculations across momentum-frequency points and also parallelize + the solving of a single large sparse matrix at each point, and thus + allowing for straightforward use of all available computational + resources.

+

The Solver allows the user to quickly evaluate the Green’s + function for a specified range of momenta and frequencies. Like the + System, it automatically checkpoints the solution (Green’s function + value) at every momentum-frequency point using + pickle, allowing for restart in case of + failure or time limits on cluster jobs.

+
+
+ + Acknowledgements +

M. R. C. acknowledges the following support: This material is based + upon work supported by the U.S. Department of Energy, Office of + Science, Office of Advanced Scientific Computing Research, Department + of Energy Computational Science Graduate Fellowship under Award Number + DE-FG02-97ER25308. This work also used theory and computational + resources of the Center for Functional Nanomaterials, which is a U.S. + Department of Energy Office of Science User Facility, and the + Scientific Data and Computing Center, a component of the Computational + Science Initiative, at Brookhaven National Laboratory under Contract + No. DE-SC0012704. S. F. and M. B. acknowledge support from the Natural + Sciences and Engineering Research Council of Canada (NSERC) and the + Stewart Blusson Quantum Matter Institute (SBQMI). A. J. M., D. R. R. + and J. S. acknowledge support from the National Science Foundation + (NSF) Materials Research Science and Engineering Centers (MRSEC) + Program through Columbia University in the Center for Precision + Assembly of Superstratic and Superatomic Solids under Grant + No. DMR-1420634. J. S. acknowledges support from the Gordon and Betty + Moore Foundation’s EPiQS Initiative through Grant GBMF8686 at Stanford + University. The Flatiron Institute is a division of the Simons + Foundation.

+

Disclaimer: This report was prepared as an account of work + sponsored by an agency of the United States Government. Neither the + United States Government nor any agency thereof, nor any of their + employees, makes any warranty, express or implied, or assumes any + legal liability or responsibility for the accuracy, completeness, or + usefulness of any information, apparatus, product, or process + disclosed, or represents that its use would not infringe privately + owned rights. Reference herein to any specific commercial product, + process, or service by trade name, trademark, manufacturer, or + otherwise does not necessarily constitute or imply its endorsement, + recommendation, or favoring by the United States Government or any + agency thereof. The views and opinions of authors expressed herein do + not necessarily state or reflect those of the United States Government + or any agency thereof.

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