In recent years, tensor network renormalization (TNR) has emerged as an efficient and accurate method for studying (1 + 1)-dimensional quantum systems or two-dimensional 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– and matrix product state–based algorithms.

Close

PrevNext

View figure in article

• Spin dynamics
• Non-Hermitian systems
• Tensor network methods
• Tensor network renormalization