【直播】【复旦理论物理报告会】Conformal geometry from entanglement

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复旦理论物理报告会Conformal geometry from entanglement

2024年5月10日 9:30



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嘉宾简介
Dr. Bowen Shi is a physics postdoc at UC San Diego, founded by Simons Collaboration on Ultra Quantum Matter. He graduated from the Ohio State University in the year 2020. His main research interest is to understand the emergence of effective theories in quantum many-body systems from the entanglement conditions on the physical wave function.报告摘要
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 (𝔠,η) 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 ground state, the quantity 𝔠 is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i) 𝔠 is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii) η is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on ground state entanglement. The stationarity of 𝔠 is equivalent to a vector fixed-point equation involving η, making our assumption locally checkable.
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