Renormalization group on tensor networks

TL;DR

This paper reviews recent tensor network methods focusing on renormalization group techniques, emphasizing their potential for studying quantum field theories and lattice QCD without sign problems.

Contribution

It summarizes recent advances in tensor network renormalization methods and discusses their applications to quantum field theory and lattice QCD, highlighting future research directions.

Findings

Tensor networks can effectively address sign problems in lattice field theories.

Recent methods enable direct investigation of universal critical behavior.

Potential applications to finite-temperature and density QCD studies.

Abstract

We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field theories, particularly with a view toward future studies of quantum chromodynamics (QCD) at finite temperature and density. They are also of broad interest in quantum field theory, with recent advances in approaches that allow one to directly investigate universal aspects of critical behavior by making use of theoretical insights from conformal field theory. We highlight several recently explored topics that are expected to play important roles in forthcoming tensor-network studies of QCD.