Analytic approaches to tensor networks for field theories



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Recording Details

Speaker(s): 
Volkher Scholz
Scientific Areas: 
Quantum Information,
Quantum Gravity,
Quantum Fields and Strings,
Quantum Matter
Collection/Series: 
Tensor Networks for Quantum Field Theories II
PIRSA Number: 
17040036

Abstract

I will discuss analytic approaches to construct tensor network representations of quantum field theories, more specifically conformal field theories in 1+1 dimensions. A key insight is that we should understand how well the tensor network can reproduce the correlation functions of the quantum field theory. Based on this measure of closeness, I will present rigorous results allowing for explicit error bounds which show that both Matrix product states (MPS) as well as the multiscale renormalization Ansatz (MERA) do approximate conformal field theories. In particular, I will discuss the case of Wess-Zumino-Witten models.

based on joint work with Robert Koenig (MPS), Brian Swingle and Michael Walter (MERA)