Critical endpoint of (3+1)-dimensional finite density $Z_3$ gauge-Higgs model with tensor renormalization group

The critical endpoint of the (3+1)-dimensional $Z_3$ gauge-Higgs model at finite density is determined by the tensor renormalization group method. This work is an extension of the previous one on the $Z_2$ model. The vital difference between them is that the $Z_3$ model suffers from the sign problem, while the $Z_2$ model does not. We show that the tensor renormalization group method allows us to locate the critical endpoint for the $Z_3$ gauge-Higgs model at finite density, regardless of the sign problem.