The ALPS project release 2.0: open source software for strongly correlated systems

In electronic systems with long-range Coulomb interaction, the nonlocal Fock-exchange term has a bandwidening effect. While this effect is included in combined many-body perturbation theory and dynamical mean field theory (DMFT) schemes, it is not taken into account in standard extended DMFT (EDMFT) calculations. Here, we include this instantaneous term in both approaches and investigate its effect on the phase diagram and dynamically screened interaction. We show that the largest deviations between previously presented EDMFT and GW +EDMFT results originate from the nonlocal Fock term, and that the quantitative differences are especially large in the strong-coupling limit. Furthermore, we show that the charge-ordering phase diagram obtained in GW +EDMFT methods for moderate interaction values is very similar to the one predicted by dual-boson methods that include the fermion-boson or four-point vertex. DOI: 10.1103/PhysRevB.95.245130 Dynamical mean field theory (DMFT) [1] self-consistently maps a correlated Hubbard lattice problem with local interactions onto an effective impurity problem consisting of a correlated orbital hybridized with a noninteracting fermionic bath. If the bath is integrated out, one obtains an impurity action with retarded hoppings. Extended dynamical mean field theory [2-10] (EDMFT) extends the DMFT idea to systems with long-range interactions. It does so by mapping a lattice problem with long-range interactions onto an effective impurity model with self-consistently determined fermionic and bosonic baths, or, in the action formulation, an impurity model with retarded hoppings and retarded interactions.While EDMFT captures dynamical screening effects and charge-order instabilities, it has been found to suffer from qualitative shortcomings in finite dimensions. For example, the charge susceptibility computed in EDMFT does not coincide with the derivative of the average charge with respect to a small applied field [11], nor does it obey local charge conservation rules [12] essential for an adequate description of collective modes such as plasmons.The EDMFT formalism has an even more basic deficiency: since it is based on a local approximation to the self-energy, it does not include even the first-order nonlocal interaction term, the Fock term. The combined GW +EDMFT [13][14][15] scheme corrects this by supplementing the local self-energy from EDMFT with the nonlocal part of the GW diagram, where G is the interacting Green's function and W the fully screened interaction. Indeed, the nonlocal Fock term [Gv] nonloc is included in the nonlocal [GW ] nonloc diagram. As described in more detail in Ref. [15] (see also the appendix of Ref.[16]), the GW +EDMFT method is formally obtained by constructing an energy functional of G and W , the Almbladh [17] functional , and by approximating as a sum of two terms, one containing all local diagrams (corresponding to EDMFT) and the other containing the simplest nonlocal correction (corresponding to the GW approximation [18]). This functional construct...

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“…617196). Part of the implementation is based on the TRIQS toolbox [63] and on the ALPS libraries [64].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

et al. 2017

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“…We acknowledge enlightening discussions with E. Kozik and M. Troyer during the development of [55,56].…”

Section: Acknowledgmentsmentioning

confidence: 99%

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Gukelberger

Werner

2015

Phys. Rev. B

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We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling diagrams up to a given order. While dynamical mean-field theory provides a good approximation for the local part of the self-energy, including its frequency dependence, the partial summation of bubble and/or ladder diagrams typically yields worse results than second-order perturbation theory. Even widely used self-consistent schemes such as GW or the fluctuation-exchange approximation (FLEX) are found to be unreliable. Combining the dynamical mean-field self-energy with the nonlocal component of GW in GW + DMFT yields improved results for the local self-energy and nonlocal self-energies of the correct order of magnitude, but here, too, a more reliable scheme is obtained by restricting the nonlocal contribution to the second-order diagram. FLEX + DMFT is found to give accurate results in the low-density regime, but even worse results than FLEX near half-filling.

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“…Th e VisTrails wiki has had over 1.5 million page views, and Google analytics reports that visitors to the site come from 65 diff erent countries. VisTrails has been adopted in several scientifi c projects, both nationally within the United States and internationally, and in diff erent areas, including environmental sciences (Baptista et al 2008, Howe et al 2008, psychiatry (Anderson et al 2007), astronomy (Tohline et al 2009), cosmology (Anderson et al 2008), high-energy physics (Dolgert et al 2008), and quantum physics (Bauer et al 2011, Freedman et al 2012. VisTrails is also a key component of the Ultrascale Visualization -Climate Data Analysis Tools (UV-CDAT), a new toolset for large-scale climate data analysis Ͻ http://uv-cdat.llnl.gov Ͼ .…”

Section: Existing Framework: Vistrailsmentioning

confidence: 99%

VisTrails SAHM: visualization and workflow management for species habitat modeling

et al. 2013

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Th e Software for Assisted Habitat Modeling (SAHM) has been created to both expedite habitat modeling and help maintain a record of the various input data, pre-and post-processing steps and modeling options incorporated in the construction of a species distribution model through the established workfl ow management and visualization VisTrails software. Th is paper provides an overview of the VisTrails:SAHM software including a link to the open source code, a table detailing the current SAHM modules, and a simple example modeling an invasive weed species in Rocky Mountain National Park, USA.Understanding where species will thrive is a useful and important consideration for resource managers concerned with either promoting (for threatened or endangered species) or controlling (for invasive or unwanted species). Th e fi eld of species distribution or habitat niche modeling is contributing to this understanding. With an increasing availability of both ecological data (Graham et al. 2004) and software packages to fi t ecological niche models (Phillips et al. 2006, Franklin 2009, Th uiller et al. 2009, Guo and Liu 2010, Peterson et al. 2011 as well as new tools to evaluate model performance (Allouche et al. 2006, Phillips and Elith 2010, Warren et al. 2010), researchers and land managers now have an unprecedented opportunity to explore many parameters and iterations for any given habitat niche modeling exercise. Each niche modeling technique has multiple parameters and options that can be adjusted and choices for input and output data. For habitat models that consider climate change, there are future climate projections from diff erent climate modeling centers and multiple emissions scenarios to consider (IPCC 2007). Land managers might want to evaluate diff erent biological responses; such as diff erent/multiple species or, for a given species, diff erent life cycles (e.g. breeding vs nesting habitat). Furthermore, it may be of interest to modify the spatial extent and spatial resolution of both input/ predictor layers and output/model results. With these options and others not listed here, the potential number of model runs and related results can be overwhelming. Th ere is a need for careful documentation of the precise model confi guration as well as meaningful interpretation of results. Scientifi c workfl ow systems help address this need.

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The ALPS project release 2.0: open source software for strongly correlated systems

Cited by 682 publications

References 55 publications

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

VisTrails SAHM: visualization and workflow management for species habitat modeling

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