Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach

TL;DR

This paper introduces a split-CTMRG algorithm for PEPS that reduces computational costs and enables large-scale variational energy optimization in quantum many-body systems.

Contribution

The authors propose a novel split-CTMRG method that maintains separate PEPS layers, lowering complexity while preserving accuracy for large bond dimension PEPS.

Findings

Significant speedups in variational energy optimization.

Maintains accuracy with reduced computational resources.

Effective for large-scale quantum lattice simulations.

Abstract

Projected entangled-pair states (PEPS) have become a powerful tool for studying quantum many-body systems in the condensed matter and quantum materials context, particularly with advances in variational energy optimization methods. A key challenge within this framework is the computational cost associated with the contraction of the two-dimensional lattice, crucial for calculating state vector norms and expectation values. The conventional approach, using the corner transfer matrix renormalization group (CTMRG), involves combining two tensor network layers, resulting in significant time and memory demands. In this work, we introduce an alternative "split-CTMRG" algorithm, which maintains separate PEPS layers and leverages new environment tensors, reducing computational complexity while preserving accuracy. Benchmarks on quantum lattice models demonstrate substantial speedups for variational energy optimization, rendering this method valuable for large-scale PEPS simulations.