Abstract
To consider interaction effects in a directed random system, we have studied a directed random XXZ model numerically. The exact diagonalizaton method is utilized to obtain distribution of complex eigenvalues. Starting from a strong non-Hermiticity limit with J z = 0, where the system becomes a non-interacting one-way model, inclusion of antiferromagnetic J z makes eigenvalues distributed on many concentric circles grouped by the number of neighboring anti-parallel spin configurations in an Ising limit. In this transition, an Ising gap opens as a result of continual recombination of spectral flows into smaller circles in the complex plane.
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