A non-Hermitian analysis of strongly correlated quantum systems

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. It is known that a non-Hermitian critical point is equal to the inverse localization length of a Hermitian non-interacting random electron system. We here conjecture that we can obtain in the same way the correlation length of a Hermitian interacting non-random system. We confirm the conjecture using exact solutions and numerical finite-size data of the Hubbard model and the antiferromagnetic XXZ model in one dimension.