DMRG Approach to Optimizing Two-Dimensional Tensor Networks

TL;DR

This paper introduces a DMRG-inspired framework for optimizing two-dimensional PEPS tensor networks, enhancing their effectiveness in quantum many-body physics problems.

Contribution

It adapts the DMRG algorithm to 2D tensor networks, filling a gap in existing optimization methods for PEPS.

Findings

Effective optimization of 2D PEPS demonstrated on spin models

Framework includes key DMRG steps for 2D tensor networks

Potential for broader applications in quantum physics

Abstract

Tensor network algorithms have been remarkably successful solving a variety of problems in quantum many-body physics. However, algorithms to optimize two-dimensional tensor networks known as PEPS lack many of the aspects that make the seminal density matrix renormalization group (DMRG) algorithm so powerful for optimizing one-dimensional tensor networks known as matrix product states. We implement a framework for optimizing two-dimensional PEPS tensor networks which includes all of steps that make DMRG so successful for optimizing one-dimension tensor networks. We present results for several 2D spin models and discuss possible extensions and applications.