DMRG Approach to Optimizing Two-Dimensional Tensor Networks

2019/08/23 by Hyatt, Katharine, Stoudenmire, E. M. · 5 citations
#FOS: Physical sciences #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.1908.08833

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.

Cited by

• Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks
• Pauli propagation enables fast classical simulation of strongly correlated quantum systems
• Computing excited states with isometric tensor networks in two-dimensions
• Diagonal Isometric Form for Tensor Product States in Two Dimensions
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation

Related

• Accelerating two-dimensional tensor network optimization by preconditioning
• Tensor Networks: a quantum-information perspective on numerical renormalization groups
• On Stability of Tensor Networks and Canonical Forms
• Modified Tucker Decomposition for Tensor Network and Fast Linearized Tensor Renormalization Group Algorithm for Two-Dimensional Quantum Spin Lattice Systems
• Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraints