Research Seminars @ Illinois

The Anthony J Leggett Institute for Condensed Matter Physics Seminar: "The entanglement bootstrap view of conformal symmetry"

Event Type

Seminar/Symposium

Sponsor

Physics Department

Location

ESB 190

Date

Oct 28, 2024   12:00 pm  

Speaker

Bowen Shi, University of Illinois Urbana-Champaign

Contact

Ljubica Milutinovic

E-Mail

ljubicam@illinois.edu

Phone

217-300-6393

Views

207

Originating Calendar

Physics - The Anthony J Leggett Institute for Condensed Matter Theory Seminar

Conformal symmetry can emerge in gapless quantum many-body systems. Such systems include 1D spin chains at the quantum critical point and the gapless edges of 2D gapped chiral topological orders. Can we detect a signature of the emergent conformal symmetry given a single ground state wave function? Can we derive (or "bootstrap") the emergence of conformal symmetry under a certain constraint on the entanglement? We report progress on deriving the validity of cross-ratio on such systems, an important signature of conformal symmetry. (Cross-ratio is a measure of distance invariant under global conformal transformations). Our assumption on the entanglement does not rely on symmetries or ways to measure geometrical distances. Instead, we utilize the "stationarity" of a quantity $c$, computable from the wave function. We argue that $c$ is the central charge. We make a few further remarks on (1) the nature of the many-body entanglement in such systems and (2) the signature of conformal dynamics related to modular flows in such systems.