All-mode Renormalization for Tensor Network with Stochastic Noise

Tensor renormalization group (TRG) is a real space coarse-graining algorithm to efficiently compute a partition function of lattice statistical models. In the process of the coarse-graining, a tensor containing local interaction is compressed using truncated singular value decomposition and the lower modes are just discarded. Such a truncation causes systematic errors and an estimation of the errors gets complicated. In order to avoid the systematic errors we propose a new technique using random noises. We present numerical experiments of the new method for 2D Ising model as a benchmark test and show its performance.