Physics (Internal)

A counterexample to the area law for quantum matter

This event is part of the Condensed Matter Theory Seminar Series.

Abstract: Entanglement is a quantum correlation which does not appear classically, and it serves as a resource for quantum technologies such as quantum computing. The area law says that the amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary of the subsystem and not its volume. A system that obeys an area law can be simulated more efficiently than an arbitrary quantum system, and an area law provides useful information about the low-energy physics of the system. It was widely believed that the area law could not be violated by more than a logarithmic factor (e.g. based on critical systems and ideas from conformal field theory) in the system’s size. We introduce a class of exactly solvable one-dimensional models which we can prove have exponentially more entanglement than previously expected, and violate the area law by a square root factor. We also prove that the gap closes as n^{-c}, where c \ge 2, which rules out conformal field theories as the continuum limit of these models. In addition to using recent advances in quantum information theory, we have drawn upon various branches of mathematics and computer science in our work and hope that the tools we have developed may be useful for other problems as well. (Joint work with Peter Shor)