From aff37086deda3e6c8710483ca974c15fec47895b Mon Sep 17 00:00:00 2001 From: nkavokine Date: Sun, 2 Jun 2024 12:36:01 -0400 Subject: [PATCH] update paper --- paper.bib | 122 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ paper.md | 28 +++++-------- 2 files changed, 133 insertions(+), 17 deletions(-) create mode 100644 paper.bib diff --git a/paper.bib b/paper.bib new file mode 100644 index 0000000..bb8cf7a --- /dev/null +++ b/paper.bib @@ -0,0 +1,122 @@ + +@article{gull2011, + title = {Continuous-time {Monte} {Carlo} methods for quantum impurity models}, + volume = {83}, + issn = {00346861}, + doi = {10.1103/RevModPhys.83.349}, + abstract = {Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean-field" approximation to the self-energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. Derivations and descriptions of the algorithms are presented in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied, and outline prospects for future applications. © 2011 American Physical Society.}, + number = {2}, + journal = {Rev. Mod. Phys.}, + author = {Gull, Emanuel and Millis, Andrew J. and Lichtenstein, Alexander I. and Rubtsov, Alexey N. and Troyer, Matthias and Werner, Philipp}, + year = {2011}, + note = {arXiv: 1012.4474}, + pages = {349--404}, + file = {PDF:/Users/nkavokine/Zotero/storage/QM73Y93K/RevModPhys.83.349.pdf:application/pdf}, +} + +@article{otsuki2013, + title = {Spin-boson coupling in continuous-time quantum {Monte} {Carlo}}, + volume = {87}, + issn = {10980121}, + doi = {10.1103/PhysRevB.87.125102}, + abstract = {A vector bosonic field coupled to the electronic spin is treated by means of the continuous-time quantum Monte Carlo method. In the Bose-Kondo model with a sub-Ohmic density of states ρB(ω)ωs with s=0.2, two contributions to the spin susceptibility, the Curie term T-1 and the term T-s due to bosonic fluctuations, are observed separately. This result indicates the existence of a residual moment and a hidden critical behavior. By including hybridization with itinerant electrons, a quantum critical point is identified between this local-moment state and the Kondo singlet state. It is demonstrated that the energy scale of the bosonic fluctuations is not affected by the quantum phase transition. © 2013 American Physical Society.}, + number = {12}, + journal = {Phys. Rev. B}, + author = {Otsuki, Junya}, + year = {2013}, + pages = {1--7}, + file = {PDF:/Users/nkavokine/Zotero/storage/B5AM3QDW/PhysRevB.87.125102.pdf:application/pdf}, +} + +@article{georges1996, + title = {Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions}, + volume = {68}, + issn = {0034-6861, 1539-0756}, + url = {https://link.aps.org/doi/10.1103/RevModPhys.68.13}, + doi = {10.1103/RevModPhys.68.13}, + language = {en}, + number = {1}, + urldate = {2023-10-27}, + journal = {Rev. Mod. Phys.}, + author = {Georges, Antoine and Kotliar, Gabriel and Krauth, Werner and Rozenberg, Marcelo J.}, + month = jan, + year = {1996}, + pages = {13--125}, + file = {Georges et al. - 1996 - Dynamical mean-field theory of strongly correlated.pdf:/Users/nkavokine/Zotero/storage/GZMWU33G/Georges et al. - 1996 - Dynamical mean-field theory of strongly correlated.pdf:application/pdf}, +} + +@article{TRIQS2015, +abstract = {We present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it. Program summary Program title: TRIQS Catalogue identifier: AEWR-v1-0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWR-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License (GPLv3) No. of lines in distributed program, including test data, etc.: 93228 No. of bytes in distributed program, including test data, etc.: 2979367 Distribution format: tar.gz Programming language: C++/Python. Computer: Any architecture with suitable compilers including PCs and clusters. Operating system: Unix, Linux, OSX. RAM: Highly problem-dependent Classification: 7.3, 20. External routines: cmake, mpi, boost, FFTW, GMP, BLAS, LAPACK, HDF5, NumPy, SciPy, h5py, mpi4py, mako. Nature of problem: Need for a modern programming framework to quickly write simple, efficient and higher-level code applicable to the studies of strongly-correlated electron systems. Solution method: We present a C++/Python open-source computational library that provides high-level abstractions for common objects and various tools in the field of quantum many-body physics, thus forming a framework for developing applications. Running time: Tests take less than a minute. Otherwise it is highly problem dependent (from minutes to several days).}, +archivePrefix = {arXiv}, +arxivId = {1504.01952}, +author = {Parcollet, Olivier and Ferrero, Michel and Ayral, Thomas and Hafermann, Hartmut and Krivenko, Igor and Messio, Laura and Seth, Priyanka}, +doi = {10.1016/j.cpc.2015.04.023}, +eprint = {1504.01952}, +issn = {00104655}, +journal = {Computer Physics Communications}, +keywords = {C++,DMFT,Many-body physics,Monte Carlo,Python,Strongly-correlated systems,ab initio calculations}, +month = {nov}, +pages = {398--415}, +title = {{TRIQS: A toolbox for research on interacting quantum systems}}, +volume = {196}, +year = {2015} +} + +@article{CTHYB2016, +author = {Seth, Priyanka and Krivenko, Igor and Ferrero, Michel and Parcollet, Olivier}, +doi = {10.1016/j.cpc.2015.10.023}, +issn = {00104655}, +journal = {Computer Physics Communications}, +month = {mar}, +pages = {274--284}, +title = {{TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems}}, +volume = {200}, +year = {2016} +} + +@article{ALPS2018, +title = {Continuous-time hybridization expansion quantum impurity solver for multi-orbital systems with complex hybridizations}, +journal = {Computer Physics Communications}, +volume = {215}, +pages = {128-136}, +year = {2017}, +issn = {0010-4655}, +doi = {https://doi.org/10.1016/j.cpc.2017.01.003}, +url = {https://www.sciencedirect.com/science/article/pii/S0010465517300036}, +author = {Hiroshi Shinaoka and Emanuel Gull and Philipp Werner}, +keywords = {Quantum impurity problems, Continuous-time impurity solver, Hybridization expansion, Complex hybridization functions, Dynamical mean-field theory}, +abstract = {We describe an open-source implementation of the continuous-time hybridization-expansion quantum Monte Carlo method for impurity models with general instantaneous two-body interactions and complex hybridization functions. The code is built on an updated version of the core libraries of ALPS (Applications and Libraries for Physics Simulations) [ALPSCore libraries]. +Program summary +Program title: ALPSCore CT-HYB Program Files doi: “ http://dx.doi.org/10.17632/dyhhx6g4md.1” Licensing provisions: GPLv3 Programming language: C++, MPI for parallelization. Nature of problem: Quantum impurity problem Solution method: Continuous-time hybridization-expansion quantum Monte Carlo External routines/libraries: ALPSCore libraries, Eigen3, Boost.} +} + +@article{w2dynamics2019, +title = {w2dynamics: Local one- and two-particle quantities from dynamical mean field theory}, +journal = {Computer Physics Communications}, +volume = {235}, +pages = {388-399}, +year = {2019}, +issn = {0010-4655}, +doi = {https://doi.org/10.1016/j.cpc.2018.09.007}, +url = {https://www.sciencedirect.com/science/article/pii/S0010465518303217}, +author = {Markus Wallerberger and Andreas Hausoel and Patrik Gunacker and Alexander Kowalski and Nicolaus Parragh and Florian Goth and Karsten Held and Giorgio Sangiovanni}, +keywords = {(continuous-time) quantum Monte Carlo, Anderson impurity model, Dynamical mean field theory, Green’s functions}, +abstract = {We describe the hybridization-expansion continuous-time quantum Monte Carlo code package “w2dynamics”, developed in Wien and Würzburg. We discuss the main features of this multi-orbital quantum impurity solver for the Anderson impurity model, dynamical mean field theory as well as its coupling to density functional theory. The w2dynamics package allows for calculating one- and two-particle quantities; it includes worm and further novel sampling schemes. Details about its download, installation, functioning and the relevant parameters are provided. +Program summary +Program title: w2dynamics Program Files doi: http://dx.doi.org/10.17632/rjs7kmjm2b.1 Licensing provisions: GNU General Public License v3 Programming language: Python, Fortran 90, and C++11 Required dependencies: cmake (≥2.8.5), MPI, LAPACK, FFTW3, Python (≥2.4) Optional dependencies: NFFT, pip, numpy (≥1.4), scipy (≥0.10), h5py, mpi4py, configobj Nature of problem: Numerically unbiased solutions of one- and two-particle propagators for quantum impurity models at finite temperature. Approximate solutions for general lattice models with strong electronic correlation. Solution method: Continuous-time quantum Monte Carlo in the hybridization expansion, including worm sampling, for the impurity problem. Dynamical mean field theory solver for the lattice problem.} +} + +@article{dumitrescu2022, + title = {Planckian metal at a doping-induced quantum critical point}, + author = {Dumitrescu, Philipp T. and Wentzell, Nils and Georges, Antoine and Parcollet, Olivier}, + journal = {Phys. Rev. B}, + volume = {105}, + issue = {18}, + pages = {L180404}, + numpages = {6}, + year = {2022}, + month = {May}, + publisher = {American Physical Society}, + doi = {10.1103/PhysRevB.105.L180404}, + url = {https://link.aps.org/doi/10.1103/PhysRevB.105.L180404} +} diff --git a/paper.md b/paper.md index 18ae89c..15909eb 100644 --- a/paper.md +++ b/paper.md @@ -33,50 +33,44 @@ optical response properties in solid-state materials. Yet, the many-electron problem is outstandingly difficult, and can be tackled analytically only when interactions are weak, or in rare exactly solvable cases. One of the popular numerical schemes for addressing strongly interacting systems is dynamical -mean-field theory (DMFT). In DMFT, the many-body problem formulated on a +mean-field theory (DMFT) [@georges1996]. In DMFT, the many-body problem formulated on a crystal lattice is self-consistently mapped onto a single atom (or impurity) immersed in an effective environment (or bath). The remaining computational task is then the solution of the impurity problem, which can be carried out -through various quantum Monte Carlo algorithms. Here, we present an implementation +through various quantum Monte Carlo algorithms [@gull2011]. Here, we present an implementation of the continous time hybridization expansion algorithm in the segment picture (`CTSEG`) based on `TRIQS`, a comprehensive library for the numerical investigation of interacting -quantum systems. +quantum systems [@TRIQS2015]. # Statement of need The Monte Carlo algorithms for quantum impurity problems are based on stochastically exploring the terms in the perturbative expansion of the solution around an exactly solvable limit. Hybridization expansion algorithms -- chief of which the -continuous-time `CTHYB` -- involve expanding around the limit of an isolated atom. +continuous-time `CTHYB` -- involve expanding around the limit of an isolated atom [@gull2011]. Three extensive libraries for the numerical treatment of quantum many-body problems are -currently available: `ALPS`, `w2dynamics` and `TRIQS`, and each has its own implementation of `CTHYB`. +currently available: `ALPS`, `w2dynamics` and `TRIQS`, and each has its own implementation of `CTHYB` +[@ALPS2018,@w2dynamics2019,@CTHYB2016]. However, a simpler and potentially faster version of the `CTHYB` algorithm, called `CTSEG`, can be used under the restriction of (possibly time-dependent) density-density interactions on the impurity. `CTSEG` can be further generalized to allow for time-dependent -spin-spin interactions. To our knowledge, no implementation of `CTSEG` has been published so far. +spin-spin interactions [@otsuki2013]. To our knowledge, no implementation of `CTSEG` has been published so far. Our `CTSEG` solver is about twice as fast as `TRIQS-CTHYB` for a single orbital problem, and has better scaling with the number of orbitals (400 times faster in our 5 orbital test case, see Fig. 1). `CTSEG` has already allowed us to obtain the first numerically-exact solution of the -quantum Heisenberg spin glass `[@Kavokine:2024]`. +quantum Heisenberg spin glass [@kavokine2024]. + +# Example of use As a further illustration of our solver's performance, we apply it to the fully connected $t-J-U$ model -studied by `[@Dumitrescu:2023]`. At half-filling, the model forms a spin glass phase, which melts into +studied by [@dumitrescu2022]. At half-filling, the model forms a spin glass phase, which melts into a metal at a doping-induced quantum critical point (QCP). Dumitrescu et al. obtained solutions at inverse temperatures up to $\beta = 65$, limited by the fermionic sign problem of their interaction expansion solver. The hybridization expansion carried out by `CTSEG` is sign-problem-free for the $t-J-U$ model, allowing us to reach $\beta = 300$ and to obtain a more accurate localization of the QCP at doping $p \approx 0.16$ (Fig. 2). -# Figures - -Figures can be included like this: -![Caption for example figure.\label{fig:example}](figure.png) -and referenced from text using \autoref{fig:example}. - -Figure sizes can be customized by adding an optional second parameter: -![Caption for example figure.](figure.png){ width=20% } - # Acknowledgements We thank Alexander Hampel for testing the code and providing valuable feedback. We thank