Jun 10 – 15, 2018
Tsinghua Sanya International Mathematics Forum
Asia/Shanghai timezone

Tensor Network Holography and Deep Learning

Jun 14, 2018, 10:30 AM
45m
Tsinghua Sanya International Mathematics Forum

Tsinghua Sanya International Mathematics Forum

Sanya, Hainan, China

Speaker

Yi-Zhuang You (UCSD & Harvard)

Description

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS_3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT_2 point).

Presentation materials