Constructing asymptotic pseudospectral atlases for interacting open quantum systems

Construct the asymptotic pseudospectral atlas for a generically interacting open quantum system, overcoming the exponential computational cost of evaluating the smallest singular value of its superoperator and justifying any truncation to low-order correlations.

Background

The paper develops the asymptotic pseudospectral atlas and evaluates it exactly for a dissipative shift chain and a chiral XY model. These solvable examples avoid the principal computational difficulty of generic many-body systems: determining the asymptotic residual requires finding the smallest singular value of a superoperator acting on an operator space whose dimension grows exponentially with system size.

For generically interacting driven open systems, the optimal operator direction may itself become increasingly complex as the system grows. Consequently, matrix-product-operator or other tensor-network approximations require rigorous justification, particularly when truncating the operator space to low-order correlations. The paper identifies this construction as an unresolved challenge and suggests driven dissipative Ising chains as an initial numerical target.