Universal Lower Bound on Topological Entanglement Entropy
Isaac H. Kim, Michael Levin, Ting-Chun Lin, Daniel Ranard, Bowen Shi
Abstract
Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that characterizes the underlying topological phase. However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase. The difference between the TEE and the value predicted by the anyon theory is often called the "spurious" topological entanglement entropy. We show that this spurious contribution is always non-negative, thus the value predicted by the anyon theory provides a universal lower bound. This observation also leads to a definition of TEE that is invariant under constant-depth quantum circuits.Received 1 March 2023Revised 14 August 2023Accepted 13 September 2023DOI:https://doi.org/10.1103/PhysRevLett.131.166601© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAnyonsExotic phases of matterOrder diagnosisTopological materialsCondensed Matter, Materials & Applied Physics