The 2016 meeting of the Simons Foundation collaboration on the many-electron problem brought together members of the collaboration, as well as experts from outside the collaboration.
The topics of the first morning revolved around improvements in techniques for studying model systems in two-dimensions. The afternoon talks focused on studies of real materials. The following morning saw presentations on ways to bring techniques for strongly correlated electrons to bear on ab initio systems.
Many of the talks highlighted benchmark model- system calculations made last year, as well as new benchmarks in preparation, including difficult regimes of the Hubbard model and one- and two-dimensional lattices of real hydrogen atoms. There were also reports of joint efforts facilitated by the many-electron collaboration, such as between the groups of Shiwei Zhang and Steven White.
“Spin, Charge and Superconducting Fluctuations in the Normal State of the Two- Dimensional Hubbard Model”
The one-electron Green function only contains partial information about a system; the two-electron Green function can be used to extract generalized susceptibilities to understand the tendency of systems to order. Using DCA on small clusters to compute susceptibilities at high and medium temperatures, James showed how this information could be used to infer likely phase transitions at lower temperatures in a quantitative way.
“Recent progress in simulating strongly correlated systems with 2D tensor network methods”
View Slides (PDF)
Philippe presented many updates on applying iPEPS (an infinite-size two-dimensional tensor network technique) to model systems. Using various unit cell sizes, he finds close competition between stripes and uniform d-wave superconductivity in t-J models. With a new truncation-error approach for extrapolation, Philippe now obtains results for the t-J model competitive with collaboration benchmarks. Finally, he highlighted the advantage of unbiased methods such as PEPS using the example of magnetization plateaux with surprising origins.
“Diagrammatic Monte Carlo approach to the Hubbard model”
Michel discussed a certain freedom in designing diagrammatic Monte Carlo calculations involving a choice to shift the non-interacting propagator. Various tests show that an optimal choice of shift greatly aids convergence. Michel offered an estimate of the pseudogap temperature in models of high Tc superconductors as well as an interpretation of how the pseudogap originates from umklapp scattering. Going forward, Michel envisions progress in finding a better scheme for summing the series rather than just pushing to higher order.
“The role of dynamic U in La2CuO4”
After giving his perspective on cuprate physics, Ferdi discussed the formalism of integrating out higher energy states at the cost of introducing a frequency-dependent interaction U (ω). To calculate this U(ω) he applied a technique known as constrained RPA (cRPA). The resulting calculations indicated that while a static U was sufficient to see a gap open in a three-band model, a dynamic U(ω) was necessary to see the same physics in a two-band model.
“Recent advances in combining DMFT with electronic structure methods”
Kristjan presented a wide overview of work from 2015, including improvements in DMFT-based methods for obtaining structural properties of materials as well as spectral properties. After arguing that the approximations made in DMFT are well suited for structural properties, Kristjan reviewed a new approach for obtaining accurate forces within DFT+DMFT, showing results for FeO and Ce. Kristjan discussed a way to understand double counting in DFT+DMFT, and compared results for densities of states obtained using DMFT based on LDA, GW, and quasiparticle self-consistent GW (QSGW).
“Simons Hydrogen benchmark project — status report”
Shiwei reported on an in-progress benchmark of several methods applied to lattices of real (3d) hydrogen atoms. All methods considered are agreeing well for one-dimensional chains. Shiwei also showed detailed checks of convergence of the methods with respect to the basis set used.
“Lattice Stability of correlated electron materials”
Ivan surveyed a number of recent works from his group using DFT+DMFT (typically based on GGA functionals), highlighting significant improvements over simply using GGAs. Applications included accurate predictions of phonon dispersions; strong changes in electronic behavior of FeSe1−xTex as a function of lattice expansion; and calculations of the metal-insulator transition in V2O3.
“Density matrix embedding applied to cuprate materials”
After reviewing his density matrix embedding theory (DMET) formalism for dealing with strongly correlated systems, primarily in two dimensions, Garnet showed how DMET performs competitively with the other methods represented in last year’s Hubbard model benchmarks. He discussed in detail the ground-state phase diagram DMET predicts for the Hubbard model. For large interaction U, his group sees complicated inhomogeneous phases between antiferromagnetic order at low doping and d-wave superconductivity at moderate doping. Garnet also reported on improved accuracy for the difficult benchmark of 1/8 filling and progress in applying DMET to ab initio cuprate systems.
“Correlations and effective interactions from first principles using quantum Monte Carlo”
Lucas introduced a novel approach developed by his group for extracting lattice model parameters from ab initio quantum Monte Carlo (QMC) calculations. A key feature of the approach is that it does not require reaching the ground state with QMC; instead, one only has to reach the regime of low-lying excited states, accessed by using different trial wavefunctions to fix the nodes. Lucas demonstrated both test calculations for small molecules and good results even for strongly correlated two-dimensional systems. The method can be used as a way to apply lattice-oriented methods such as tensor networks to ab initio systems.