Institute of Physics, Czech Academy of Sciences

Na Slovance 2, CZ-182 21 Prague, Czech Republic

- quantum Monte Carlo (QMC) methods for electronic structure calculations
- review article on applications of QMC methods in solids:
J.K. & L. Mitas,
Rep. Prog. Phys.
**74**, 026502 (2011) - properties of deep Earth materials under extreme conditions
- model description of cold atomic systems, BCS–BEC crossover
- contributions to the quantum Monte Carlo code QWalk (browse repository)
- simple simulations I did some time ago to get started with the method

- review article on applications of QMC methods in solids:
J.K. & L. Mitas,
Rep. Prog. Phys.
- electronic structure of compounds with strongly correlated electrons
- dynamical mean-field theory (DMFT) and beyond
- applications of the LDA+DMFT method to transition-metal, rare-earth and actinide compounds
- analysis of the core-level spectra in the LDA+DMFT framework
- development of the exact-diagonalization (Lanczos) solver for the multi-orbital Anderson impurity model

- transport in disordered systems
- diagrammatic approximations for two-particle vertex functions
- evolution of electronic states from weak to Anderson localization

The following examples show a few details, more can be found in the papers linked in the publication list.

Pressure–volume equation of state of crystalline iron oxide calculated
using diffusion quantum Monte Carlo method (lines),
Phys.
Rev. Lett. **101**, 185502 (2008). (In collaboration with
Lubos Mitas, NCSU.)

*Legend:* rock salt (B1) structure stable at low pressures (red line),
NiAs (iB8) structure stable at high pressures (blue line), B1 experimental
data (circles), iB8 experimental data (squares). Diffusion Monte Carlo
predicts the transition pressure Pc at approximately 65 GPa, providing
substantial improvement compared to DFT based approaches.

Phase diagram for an impure crystal calculated from our proposal of a
mean field theory for disordered electronic systems,
Phys. Rev. B
**71**, 033103 (2005), *ibid.*
245106 (2005). (In collaboration with
Vaclav Janis, FZU AV CR.)

*Legend:* energy of quantum state (x-axis), measure of disorder strength
(y-axis), band edge (black line), mobility edge (red line),
localized/non-diffusive states (hatched area), extended/transport states
(white “egg”)

Exercises that accompany undergraduate course of Thermodynamics and Statistical Physics (Faculty of Mathematics and Physics, Charles University, Prague) – somewhat outdated (I was doing this in years 2002–2005), but might not be completely useless if you understand Czech.