Conformal geometry from entanglement

Understand

In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short).

• We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap.
• We introduce a novel pair of information-theoretic quantities $(\mathfrak{c}_{\mathrm{tot}}, \eta)$ that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure.
• We posit that, for a topological groundstate, the quantity $\mathfrak{c}_{\mathrm{tot}}$ is stationary under arbitrary variations of the quantum state, and study the logical consequences.