Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions

TL;DR

This paper introduces a renormalization algorithm for quantum many-body systems in higher dimensions using projected entangled-pair states, enabling efficient computation of correlations and advanced simulations of spin systems.

Contribution

It develops a novel algorithm for correlation functions in higher-dimensional quantum systems using PEPS, enhancing simulation capabilities.

Findings

Efficient computation of correlation functions in 2D and higher dimensions.

Simulation of ground states, finite temperature, and evolution of spin systems.

Demonstrated effectiveness of the method in complex quantum systems.

Abstract

We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We use this result to build powerful numerical simulation techniques to describe the ground state, finite temperature, and evolution of spin systems in two and higher dimensions.