Abstract:
Tensor network renormalization group (RG) is a powerful technique providing great control over the renormalization group flow both numerically and analytically. This talk will focus on the study of fixed points of tensor network RG maps in the context of classical lattice models (e.g., the Ising model). Studying fixed points allows one to retrieve information about phase transitions in a system, which motivates this research. I will first introduce basic tensor network concepts. Then, I will present some rigorous results about high- and low-temperature fixed points of lattice spin models (based on arXiv:2107.11464, 2210.06669, and 2401.04229). Finally, I will discuss the recent development that may grant access to the critical fixed points of lattice systems (based on arXiv:2408.10312).
