Iterative Compression-Decimation Scheme for Tensor Network Optimization

Tensor network methods are now a widely used tool in several branches of theoretical physics, particularly in the area of strongly correlated systems. The main obstacle in employing these techniques to solve hard (classical or quantum) strongly correlated problems is the need to fully contract a tensor network to obtain physical quantities of interest, such as observables or partition functions. Several elaborate strategies to perform the tensor network contraction have been developed in the past few years. However, important classes of systems, such as systems lacking translational invariance or systems with arbitrary boundary conditions, have so far remained mostly outside the scope of tensor network techniques. In this talk, I will describe a simple yet powerful scheme, called iterative compression-decimation (ICD), to perform full tensor network contractions in systems with disorder and / or arbitrary boundaries [1]. The algorithm iteratively removes redundancies in tensor entries due to either short range entanglement or constrains imposed locally and, more importantly, globally at the boundary. I will demonstrate the efficiency of the method in solving hard computational problems and in simulating quantum dynamics via a 1+1D tensor network representation of the history of a one-dimensional quantum state.

[1] Z.-C. Yang, S. Kourtis, C. Chamon, E. R. Mucciolo, and A. E. Ruckenstein, arXiv:1708.08932 (2017).