Efficient Classical Simulation of Many-body Systems with Local Integrals of Motion

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" summary

Claim: a complete set of strictly local integrals of motion lets one build a spectral matrix product operator that encodes every eigenstate as choices of extra indices; in 1D the projector MPO is exact and local expectation values cost only O(N) to evaluate, and time evolution from any MPS-representable initial state is accessible via perfect sampling of eigenstate weights so arbitrarily large times are reachable; in higher D the spectral PEPS exists but contraction becomes nonprovable; if one also has local conjugate variables then all tasks become efficiently solvable in any dimension.

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" chapters (8)

1. 0:00Introduction
2. 0:45Motivation
3. 4:48Localization
4. 22:07Efficient Classical Simulation
5. 24:17Spectral Tensor Network
6. 30:57Maximum Entropy
7. 38:27Locality
8. 43:37Representation

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