Citation: Shi, Bowen. "Verlinde formula from entanglement." Physical Review Research 2.2 (2020): 023132.
Web: https://arxiv.org/abs/1911.01470
Tags: MTC-reconstruction
This paper reconstructs the S-matrix as part of the entanglement bootstrap programme, shows that it is unitary, and that it satisfies the Verlinde formula.
This paper is a major win for the entanglement bootstrap programme. The definition is clean, concise, and manifestly well-defined. The Verlinde formula then follows from a not-too-difficult but still nontrivial argument about entropy maximization and quantum state merging, just like with most of the bootstrap programme.
This work is especially an accomplishment when compared with the 2015 work of Haah:
> Haah, Jeongwan. "An invariant of topologically ordered states under local unitary transformations." Communications in Mathematical Physics 342 (2016): 771-801.
In a way, both papers do the same thingL they give microscopic definition of the S-matrix from a ground state wavefunction and argue that it must be the S-matrix. Shi's construction is manifestly well-defined, has an easy-to-predict proof structure, and fits into a 6-page paper. Haah's construction takes a long to to prove-well-definiteness, relies on algebra of "locally invisible operators", and takes 43 pages.