A non-Hermitian analysis of strongly correlated quantum systems.

We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. We conjecture that the non-Hermitian critical point where the energy gap vanishes is equal to the inverse correlation length of the Hermitian system. We confirm the conjecture for three exactly solved models analytically and for an unsolved model numerically. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]