Time-reversal positivity

We propose a new analytical tool called time-reversal positivity. It is an analogue of the Majorana reflection positivity in time-reversal symmetric case. This new time-reversal positivity can fully explain the relationship between time-reversal symmetry and the sign-free property in quantum Monte Carlo simulations. Using a cone-theoretical method, we show the ground state uniqueness for the time-reversal symmetric non-hermitian Hubbard model.