Presentations

I will review some applications of entanglement entropy (EE) and entanglement spectra (ES) in quantum many-body systems. In a variety of topological phases, it has been found that the ES has a similar structure as the edge-mode spectrum. The "cut and glue" picture gives a physical explanation of this remarkable entanglement-edge correspondence [1]. I will explain a simple formulation of this picture based on two coupled (chiral) Tomonaga-Luttinger liquids [2]. The obtained ES can be used to derive the so-called topological entropy. In systems with continuous symmetry breaking, the EE shows a subleading logarithmic term whose coefficient is related to the number of Nambu-Goldstone modes [3]. Furthermore, the ES shows a "tower of states" structure reminiscent of the finite-size energy spectrum. I will explain the emergence of analogous features in the intercomponent entanglement in binary Bose-Einstein condensates [4]. [1] X.-L. Qi, H. Katsura, and A.W.W. Ludwig, Phys. Rev. Lett. 108, 196402 (2012). [2] R. Lundgren, Y. Fuji, S. Furukawa, and M. Oshikawa, Phys. Rev. B 88, 245137 (2013). [3] M. A. Metlitski and T. Grover, arXiv:1112.5166. [4] T. Yoshino, S. Furukawa, and M. Ueda, Phys. Rev. A 103, 043321 (2021).