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In recent years, tensor network renormalization (TNR) has emerged as anefficient and accurate method for studying (1+1)D quantum systems or 2Dclassical systems using real-space renormalization group (RG) techniques. Onenotable application of TNR is its ability to extract central charge andconformal scaling dimensions for critical systems. In this paper, we presentthe implementation of the Loop-TNR algorithm, which allows for the computationof dynamical correlation functions. Our algorithm goes beyond traditionalapproaches by not only calculating correlations in the spatial direction, wherethe separation is an integer, but also in the temporal direction, where thetime difference can contain decimal values. Our algorithm is designed to handleboth imaginary-time and real-time correlations, utilizing a tensor networkrepresentation constructed from a path-integral formalism. Additionally, wehighlight that the Loop-TNR algorithm can also be applied to investigatecritical properties of non-Hermitian systems, an area that was previouslyinaccessible using density matrix renormalization group(DMRG) and matrixproduct state(MPS) based algorithms.

Tensor network renormalization: application to dynamic correlation functions and non-hermitian systems