Seminar of Physics - Luboš Mitáš (30.5.2017)
Tuesday 30.5.2017 at 14:00, Lecture room F2/272
Luboš Mitáš (North Carolina State University):
Quantum Monte Carlo many-body methods: introduction and recent progress in fixed-node vs. fixed-phase and variable spins formulations
Abstract:
We will present a short introduction into the electronic structure quantum Monte Carlo (QMC) based on sampling of particles coordinates. These methods typically employ fixed-node approximations to deal with the fermion signs. We will show examples of current such calculations that encompass strongly correlated systems, molecules, ultracold atomic condensates, etc, together with insights into biases generated by the fixed nodes in general. So far, however, such QMC calculations have been limited to static, collinear treatment of electronic spins. Recently, we have developed QMC with variable spins for calculations that involve spin-orbit or other spin-dependent Hamiltonians. For corresponding inherently complex wave functions the fixed-node condition can be recast into a fixed-phase formulation. Interestingly, the constructed spinor-based wave functions contain the fixed-node solution as a special case and therefore cover both cases as particular limits. We will point out applications and also attractive properties of the developed fixed-phase method: i) it transforms the fermionic calculation into a bosonic one in a state-specific, many-body, effective potential; ii) it makes the sampling ergodic by construction; iii) it is variational and constructively improvable. Lastly, I will briefly talk about the nodes of eigenstates due to their both fundamental and practical implications for the fixed-node/phase methods. For example, we found several relationships between eigenvalues and nodes/phases such as new types of averages over nodal domains and hypersurfaces that alternatively determine the eigenvalues of exact eigenstates.