CyGutz solves a generic multi-band Hubbard model (including local correlated orbitals and nonlocal orbitals) using the Gutzwiller rotationally invariant slave-boson method (G-RISB). CyGutz can handle (tight-binding) models and has an interface to WIEN2k to treat realistic materials with different degrees of electron correlations. CyGutz yields ground properties with comparable accuracy to DFT+DMFT(+CTQMC), but it is over two-orders of magnitude faster. It can handle all the possible local symmetries without introducing further approximations. CyGutz consists of programs, executables, and scripts written in Fortran90, C (C++), and Python 2.7. The stable version of the CyGutz package is open source under a BSD license and is available for download while the version in active development is available upon request.

The basic idea of G-RISB is to introduce a Gutzwiller projector to variationally optimize the local reduced many-body density matrices in order to take into account the competition between the local Coulomb potential energy and the non-local kinetic energy. G-RISB shares ideas with LDA+DMFT and slave boson theory: The (LDA+) rotationally invariant slave boson method is equivalent at the mean field level to the (LDA+) Gutzwiller approximation. The latter can be viewed as a special case of LDA+DMFT [Phys. Rev. X 5, 011008 (2015)].

To reach a self-consistent solution, CyGutz starts with the setup of a generic [Kohn-Sham]-Hubbard model based on the input bare band energies and the specified local correlated orbitals, which are expressed in terms of the bare band wave functions. Here the bare bands can be obtained from LDA calculations or tight-binding models. The solution of the generic Hubbard model is then cast as a root-finding problem within the Gutzwiller-Slave-Boson method [Phys. Rev. X 5, 011008 (2015)]. For DFT+G-RISB calculations, the Gutzwiller renormalized electron density is evaluated as a feedback to the outer charge self-consistency loop. 

Capabilities of CyGutz:

• The code includes a sparse-matrix based exact diagonalization (ED) solver. A Hartree-Fock solver is also included for testing and debugging purpose.
• G-RISB calculates ground state properties of strongly correlated systems. It can produce the total energy, the Gutzwiller quasi-particle spectral function, as well as the local reduced many-body density matrices (e.g. multiplet structures). 

Features of CuGutz:

• The code uses the most general form of the Gutzwiller wave function and the Gutzwiller approximation: it can take into consideration all local interactions.
• It can handle all the cases where the self-energy has only nonzero diagonal elements, which includes, e.g. paramagnetic states of f-electron systems with negligible crystal filed splitting, and paramagnetic/magnetic states of d-electron systems with cubic symmetry.
• It performs parallelization over k-points and equivalent correlated atoms using open-MPI. Therefore it can solve large systems as are treatable in the (WIEN2k)-DFT code (unit cell of ~100 atoms).
• G-RISB can treat Mott insulators and orbital selective Mott transitions (OSMT). The latter goes beyond the known solution to describe the Mott transition in the single-band Hubbard model, and can describe OSMT in the most general multi-correlated orbital systems. The rotational invariance of the new technique has been explicitly utilized, without the necessity to be constrained to one particular orbital orientation.
• A set of pre-analysis and post-processing python scripts to set up the calculations and to analyze the results is now in place for users to facilitate the packages for complicated models and materials. The python tools include the initialization of the solver, the method to construct a general tight-binding model, local symmetry analysis for the impurity problem, and ways to get the various local physical quantities based on the density matrix.

Related Publications

Slave Boson Theory of Orbital Differentiation with Crystal Field Effects: Application to UO2.
Nicola Lanatà, Yongxin Yao, Xiaoyu Deng, Vladimir Dobrosavljević, and Gabriel Kotliar,
Phys. Rev. Lett. 118, 126401 (2017)

Phase Diagram and Electronic Structure of Praseodymium and Plutonium
Nicola Lanatà, Yongxin Yao, Cai-Zhuang Wang, Kai-Ming Ho, and Gabriel Kotliar,
Phys. Rev. X 5, 011008 (2015)