Sign problems and tensor renormalization group

Sign problems appear generically in simulating a system with a high density of fermions, where the Boltzmann weight oscillates fast. Sign problems also occur in modes with complex couplings or temperature. It remains a challenging problem for Monte Carlo practitioners in condensed matter physics and particle physics. In this talk, I will present our latest results on calculating lattice spin models with complex coupling via numerical tensor renormalization group method. I will also present results on two dimensional XY (or O(2)) model with a complex ``chemical potential'' term. Comparison with the world-line algorithm will be shown and a discussion on possible extension of the tensor renormalization group method to models in other gauge groups and higher dimensions will be followed.