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• What is the current state of the art of QMC as compared to other many-body techniques? Is it possible to imagine QMC as a reliable standard to be used also by non- experts in the near future? What is the cost/benefit ratio compared, for instance, to DFT calculations?
• Is it possible to extend the concept of “chemical accuracy” beyond quantum chemistry problems? Can QMC methods meet these requirements in general?
• Each QMC flavor for T=0 problems has pros and cons. Is there systematic evidence pointing to some efficiency criterion that can be used to discriminate among different techniques? Or is it really just a matter of personal taste?
• In the case of calculations of finite systems (atoms, molecules, nuclei, clusters) what is the comparison in terms of accuracy and efficiency with few-body methods? Up to which number of particles is reliable benchmarking possible?
• For infinite systems, what is the limit of projection methods in terms of number of particles to be treated? Is the extrapolation to the thermodynamic limit under control? How does this depend on the particular system studied? Do we just need bigger computers or better algorithms?
• A “sign problem” arises in any Monte Carlo method with fluctuating positive and negative weights. Is it possible to construct a hierarchical ‘taxonomy’ of the various sign problems that arise in QMC ranked by severity and the potential for amelioration or removal of the problem?
• For many-fermion systems, how can the systematic error due to the sign problem be estimated? Have we definitely and mathematically proven that the DMC sign-poblem is always intractable (see Troyer’s conjecture)?
• Does it make sense to search for algorithms that go in the direction of getting a longer transient, or is it better to rely on wavefunction optimization (in a broad sense, including projection methods on basis sets)?
• Is there any use of the knowledge that has been gathered about the nodes of a many-fermion wavefunction?
• Recently many proposals have been made of algorithms working in some “dual” space. Is this the future direction of QMC? Is QMC in configuration space still a good choice?
• What about QMC in reciprocal space? Can we systematically study problems with non-local interactions?
• Non-local interactions also appear when an effective Hamiltonian is constructed by integrating out a (typically frozen) degree of freedom. This form of approximation is used extensively in condensed matter applications where core electrons are replaced by a pseudo-potential. How general is this approach? Can the resulting non-local interactions be evaluated exactly without invoking a trial field to ‘localize’ the action? Can the development of pseudo-potentials within the many-body framework afforded by QMC be made systematic?
• What is the state of the art concerning QMC for Hamiltonians breaking time reversal symmetry (e.g. inclusion of magnetic fields)?
• Nuclear physics calculations require the use of Hamiltonians depending on spin/isospin operators. What kind of extensions towards condensed matter problems can be considered?
• What is the status of the application of QMC to the study of excited states?
• Can we systematically obtain information about the response function of a many- body system from QMC? Recent applications on hydrogen, confined electron systems and nuclei are extremely promising. Some old calculations exist for 4He. How far can wse go along this line?
• How far are we from an efficient QMC-based ab initio molecular dynamics? What are the costs/benefits of such an approach relative to e.g. perturbative correction of DFT generated MD ensemble averages using QMC energies.
• What is the status of finite temperature calculations? PIMC methods are now very efficient, also thanks to the introduction of grand-canonical averaging (worm algorithm) and Hybrid Monte Carlo.
• How reliable are the approximations made for many-fermion PIMC calculations?
• Which kind of improvements do we need to efficiently extend the range of temperatures below the current limits? For example, in ground state methods where the focus is on a single eigenstate, importance sampling based on trial / guiding functions provides a dramatic improvement in efficiency. Can such an approach be systematically generalized to the finite temperature case where the fundamental object of interest is a density matrix?