# Loop update for infinite projected entangled-pair states in two spatial dimensions

## TL;DR

This paper introduces an improved method for imaginary time evolution of infinite projected entangled-pair states (iPEPS), enhancing accuracy for critical systems by using cyclic optimal truncation along a closed loop.

## Contribution

It presents a novel cyclic optimal truncation technique for tensor updates in iPEPS, applicable to both simple and full update strategies, improving simulation of quantum lattice models.

## Key findings

- Enhanced simulation accuracy for critical quantum systems
- Effective tensor update scheme demonstrated on Heisenberg and Ising models
- Applicable to both simple and full update methods

## Abstract

We propose an improved approach to carry out the imaginary time evolution of infinite projected entangled-pair states (iPEPS), especially for systems with criticality. A cyclic optimal truncation is introduced to update the tensors along a closed loop, aiming to remove the redundant internal correlations. We demonstrate the algorithm by considering an elaborate evolution based on simple update on a small plaquette. This scheme can also be applied to a full update strategy. We demonstrate their performances on simulating the ground states of the spin-$1/2$ anti-ferromagnetic Heisenberg model and the transverse field Ising model on a square lattice.