  In recent years, tensor network renormalization (TNR) has emerged as an
efficient and accurate method for studying (1+1)D quantum systems or 2D
classical systems using real-space renormalization group (RG) techniques. One
notable application of TNR is its ability to extract central charge and
conformal scaling dimensions for critical systems. In this paper, we present
the implementation of the Loop-TNR algorithm, which allows for the computation
of dynamical correlation functions. Our algorithm goes beyond traditional
approaches by not only calculating correlations in the spatial direction, where
the separation is an integer, but also in the temporal direction, where the
time difference can contain decimal values. Our algorithm is designed to handle
both imaginary-time and real-time correlations, utilizing a tensor network
representation constructed from a path-integral formalism. Additionally, we
highlight that the Loop-TNR algorithm can also be applied to investigate
critical properties of non-Hermitian systems, an area that was previously
inaccessible using density matrix renormalization group(DMRG) and matrix
product state(MPS) based algorithms.

Strongly Correlated Electrons;Quantum Physics