## Holmes

** Adam Holmes **(Laboratory of Atomics and Solid State Physics, Cornell University)

**Efficient heat-bath sampling in Slater determinant space**

2016/10/7 (Fri) 14:30 - 15:30 Science and Technology Research Building #4 807 Seminar Room

**Abstract**

The variational solution of the many-body Schodinger equation in a basis of Slater determinants - called Full Configuration Interaction (Full CI) - is computationally intractable for all but the smallest systems, as the number of Slater determinants scales combinatorially with the number of particles and single-particle basis functions. Because of this, many clever methods have been devised to explore important subsets of the Full CI space without requiring its storage. Examples include stochastic methods, such as Full CI Quantum Monte Carlo (FCIQMC) and Model Space Quantum Monte Carlo (MSQMC). However, many of these methods explore the Full CI space in an inefficient manner: they treat Slater determinants connected to a reference by nonzero Hamiltonian matrix elements on "equal footing," by sampling them with uniform probability. It is much more efficient to sample the more important Slater determinants more frequently (so-called heat-bath sampling), but it is too expensive to exactly construct the required probability distribution every time a new determinant is used as a reference. In this talk, I describe a solution to this problem: an efficient algorithm for performing approximate heat-bath sampling. I then demonstrate that it dramatically improves the efficiency of FCIQMC, and comment on how I believe it will improve the efficiency of MSQMC even more dramatically.