A Unification of Information and Matter

Abstract

In this book, our discussions on many-body quantum systems have been concentrated on gapped topological states. After the introduction of the concept of long-range quantum entanglement and the discovery of related mathematical theories (such as tensor category theory), a systematic understanding of all gapped states in any dimensions is emerging, which include topological orders and SPT orders. However, our understanding of highly entangled gapless states is very limited. We do not even know where to start, to gain a systematic understanding of highly entangled gapless states. This will be the next big challenge in condensed matter physics. In this chapter, we will study some examples of highly entangled gapless states. We will show that long-range entangled qubits can provide a unified origin of light and electrons (or more generally, gauge interactions and Fermi statistics): light waves (gauge fields) are fluctuations of long-range entanglement and electrons (fermions) are defects of long-range entanglement. Since gauge bosons and fermions represent almost all the elementary particles, the above results suggest that the space formed by long-range entangled qubits may be an origin of all matter. In other words, (quantum) information unifies matter. This happens to be the central theme of this book: a theory of quantum information and quantum matter.