Rostock 2019 – wissenschaftliches Programm
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A: Fachverband Atomphysik
A 31: Quantum gases (Fermions) (joint session A/Q)
A 31.7: Vortrag
Donnerstag, 14. März 2019, 15:30–15:45, S HS 1 Physik
Easing the sign problem — •Dominik Hangleiter1, Ingo Roth1, Daniel Nagaj2, and Jens Eisert1 — 1Freie Universität Berlin, 14195 Berlin — 2Slovak Academy of Sciences, Bratislava, Slovakia
Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, their ground and thermal state properties. The idea lying at the heart of QMC methods is to sample out expectation values or partition functions by expanding these quantities in a basis. However, such methods face a severe limitation for many quantum systems, in particular so for fermionic systems. This limitation has been dubbed the `sign problem' of QMC, referring to the situation in which the distribution to be sampled from is non-positive. Here, we take a systematic approach towards alleviating the sign problem by local basis changes, realising that it is a basis-dependent property. Going beyond previous work on exactly `curing' the sign problem, we consider the optimization problem of finding the basis in which the sign problem is smallest and refer to this problem as `easing' the sign problem. We then show that easing the sign problem can be a computationally hard task, even in situations in which finding an exact solution or deciding if such a solution exists is easy.