Speaker: Tomohiro Soejima (UC Berkeley)

Date & Time: 2-3pm, July 3, 2019.

Room: Seminar Room A&D (Engineering Building #6)

Title: Isometric tensor network representation of string-net liquids and multipartite entanglement

Abstract: Efficient numerical simulation of 2D quantum systems remains an open question. Recently, a new variational wavefunction called Isometric Tensor Network States (ITNS) was proposed, motivated by 2D Projected-Entanglement Pair States (PEPS) and 1d Matrix Product States (MPS). The wavefunction allows for efficient evaluation of local expectation values, and therefore has a possibility to realize an efficient algorithm.

In this talk, we will review the basics of ITNS and show that string-net liquids as defined by Levin-Wen [1] can be put in an ITNS. We further show that application of finite depth unitary circuit will maintain isometry. This implies, in particular, that any wavefunction that has abelian topological order with gappable edges can be represented as ITNS.

In the last part of the talk, I will discuss some of more exploratory result on multipartite entanglement and boundary condensate of string-net liquid, calculated using the ITNS representation.

[1] Levin, M; Wen, X. G.; Phys. Rev. B 71, 045110