Exact Holographic Mapping and Emergent Space-time Geometry
summary
Proposes a constructive, unitary tensor-network mapping from a D‑dimensional many‑body state to a higher‑dimensional “bulk” and defines bulk distances from correlation decay (distance ≈ −log correlation). Implements it for 1D free fermions by building an explicit Exact Holographic Mapping that becomes a wavelet basis on the boundary, uses mutual information and imaginary‑time correlators, recovers AdS3 geometry for the critical ground state and produces a Euclidean black‑hole (time circle shrinking) at finite temperature. The construction is explicit and numerically verified for these examples.
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chapters (8)
- 0:00Intro
- 7:00General Principles
- 15:00Example
- 17:50Explicit formula
- 20:30Long distance
- 36:00Mera
- 41:15Correlation
- 49:30Heart Wavelet
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