Bold diagrammatic Monte Carlo and unbiased analytic continuation methods to get unbiased solutions for many-particle problems

by Dr Andrey S. Mishchenko (RIKEN)

Monday 18 Jan 2016, 13:30 → 14:30 Asia/Tokyo

Main Research Building 433 (RIKEN Wako)

Date: Jan 18 (Mon) Time: 13:30 - Place: Main Research bldg. 433 Speaker: Andrey S. Mishchenko (RIKEN) Title: Bold diagrammatic Monte Carlo and unbiased analytic continuation methods to get unbiased solutions for many-particle problems Abstract: Accurate unbiased solution for a problem of polarons at finite densities was missing because numerous avoiding approximations approaches were disabled by famous Fermion sign problem. Recently developed Bold Diagrammatic Monte Carlo (BDMC) technique [1] circumvents sign problem. It is capable of giving accurate unbiased results in the range from a single polaron to a dense system. The technique is successful even in the most difficult regime when Fermi energy is equal to phonon frequency and where other numeric and analytic techniques fail. We describe the technique, results, and prospects of further applications of the method. Excited states of the system can be studied if one can make accurate unbiased analytic continuation of the Green function or/and current-current correlation function from imaginary times to real frequencies. Popular Maximal Entropy method often fails because it is significantly biased by the so called default model. We developed a novel method based on a hybrid of Stochastic Optimization [2,3] and Consistent Constraints [4] methods. The novel method is absolutely unbiased and gives possibility to get unbiased results even for such elusive problem as polaron mobility [5]. References 1. A. S. Mishchenko, N. Nagaosa, and N. Prokof’ev, Phys. Rev. Lett. 113, 166402 (2014). 2. A. S. Mishchenko, N. V. Prokof’ev, A. Sakamoto, and B. V. Svistunov, Phys. Rev. B 62, 6317 (2000). 3. A. S. Mishchenko, Stochastic optimization method for analytic continuation, contribution to "Correlated Electrons: From Models to Materials", ed. by E. Pavarini, W. Koch, F. Anders and M. Jarrell, pp. 14.1-14.28, (Forschungszentrum J ulich GmbH, Julich, 2012). 4. N. V. Prokof’ev, B. V. Svistunov, JETP Lett. 97, 649 (2013). 5. A. S. Mishchenko, N. Nagaosa, G. De Filippis, A. de Candia, and V. Cataudella, Phys. Rev. Lett. 114, 146401 (2015). See more QHP seminars