Abstract
We discuss quantum systems of large system size N, in particular, the \(N\rightarrow \infty \) limit (thermodynamic limit). We call them the quantum many-body systems. We ask about the physical properties of these quantum many-body systems in the thermodynamic limit. Our main focus in this chapter will be many-body systems with an energy gap and the entanglement properties of their ground states. We introduce the entanglement area law and its constant correction—the topological entanglement entropy. We discuss the information-theoretic meaning of topological entanglement entropy, and generalize it to construct a “universal entanglement detector”, whose values on the gapped ground states provide nontrivial information of the system.
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