Entanglement in Many-Particle Systems Kun Yang, Florida State University, DMR 1004545

1. Entanglement in Many-Particle SystemsKun Yang, Florida State University, DMR 1004545 Entanglement is the most counter-intuitive aspect of quantum mechanics. The most widely used measure of entanglement is entanglement entropy. For most extended quantum systems entanglement entropy follows the area law, which states that it is proportional to the surface area of the subsystem. However, violations of the area law, usually in a logarithmic fashion, do exist. They are found in quantum critical 1D systems. The only established examples of such violation in higher dimensions are free fermion states with Fermi surfaces, where it is found that the area law is enhanced by a logarithmic factor. In a recent work, we explored the relation between logarithmic divergence in 1D fermionic systems and that of free fermions in higher dimensions. We show that both logarithmic factors share the same origin - the singularity at the Fermi points or Fermi surface. We then make use of the tool of multi-dimensional bosonization to re-derive the entanglement entropy of free fermions in high dimensions in a simpler way. Furthermore the bosonization technique allows us to take into account the Fermi liquid interactions, and obtain the leading scaling behavior of the entanglement entropy of Fermi liquids. The central result of our work is that Fermi liquid interactions do not alter the leading scaling behavior of the entanglement entropy, and the logarithmic enhancement of area law is a robust property of the Fermi liquid phase. Illustration of relation between one-dimensional and higher dimensional entanglement through an array of decoupled fermion chains and the corresponding Fermi surfaces.

2. Entanglement in Many-Particle Systems Kun Yang, Florida State University, DMR 1004545 Personnel Development: The PI’s graduate student, Wenxin Ding, has been actively involved in this work. In fact this work forms the central piece of Ding’s Ph.D. dissertation, which he successfully defended in summer 2012. This summer the PI also picked up a new student, Mohammad Pouranvari, who will continue working on entanglement. Outreach activities: The PI served as a research sponsor of FSU's Young Scholars Program during summer 2012. This is a residential science and mathematics program for Florida high-school students with significant potential for careers in the sciences, engineering and health professions. The PI was the research sponsor of Somya Sha, a rising senior from Miami. During his 6-week stay at FSU Sha interacted actively with the PI and his students, and got to learn about some basic quantum mechanics, and appreciate entanglement. Picture: Pouranvari (left) and Sha discussing entanglement.