Matrix product approximations to conformal field theories

Robert König, Volkher B. Scholz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We establish rigorous error bounds for approximating correlation functions of conformal field theories (CFTs) by certain finite-dimensional tensor networks. For chiral CFTs, the approximation takes the form of a matrix product state. For full CFTs consisting of a chiral and an anti-chiral part, the approximation is given by a finitely correlated state. We show that the bond dimension scales polynomially in the inverse of the approximation error and sub-exponentially in inverse of the minimal distance between insertion points. We illustrate our findings using Wess–Zumino–Witten models, and show that there is a one-to-one correspondence between group-covariant MPS and our approximation.

Original languageEnglish
Pages (from-to)32-121
Number of pages90
JournalNuclear Physics, Section B
StatePublished - Jul 2017


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