Computing Lattice Field Theory by Tensor Networks―Challenge to Sign Problem

Abstract

We review how tensor networks are used in quantum field theory on the lattice. The striking feature of the method is free of the sign problem which is a serious drawback of the Monte Carlo method. In fact the tensor networks have been applied and verified mainly in two dimensional system. On the other hand, the computation cost of the tensor networks is known to be severe for higher dimensional system. Recently, however, thanks to the progress of the coarse-graining algorithm, tensor network studies of the four dimensional system with simple internal degree of freedom have just started. We hope that further algorithmic developments make the tensor network computation of lattice QCD feasible.