Matrix Product States in Quantum Spin Chains

TL;DR

This paper introduces an advanced mathematical framework for representing matrix product states (MPS) in infinite quantum systems, enhancing understanding and manipulation of complex quantum states like GHZ states.

Contribution

It develops a new compatibility condition within quasi-local algebras, allowing finite MPS to be extended to infinite-volume states, which is a novel theoretical advancement.

Findings

Extended MPS framework for infinite systems

Application to GHZ state demonstrates method's effectiveness

Potential for improved quantum information processing

Abstract

In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we enable the extension of finite MPS to an infinite-volume state, providing new insights into complex, high-dimensional quantum systems. As an illustrative example, we apply this method to the Greenberger-Horne-Zeilinger (GHZ) state. This approach offers significant potential for advancing theoretical frameworks and practical methodologies in the field of quantum information.