Tensor-network Approach to Critical Systems in 1+1 Dimensions

by Masaki Oshikawa (University of Tokyo)

Thursday Jun 12, 2025, 2:00 PM → 3:00 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Tensor networks including Matrix Product States are powerful tools to investigate quantum many-body systems as well as classical statistical systems, both in conceptual and computational aspects. However, in many cases there are limitations to approach critical systems due to finite bond dimensions. This problem can be circumvented by combining the tensor-network calculation with finite-size scaling of Conformal Field Theory. On the other hand, the effect of the finite bond dimensions can be understood in terms of emergent relevant perturbation to the Conformal Field Theory. I will demonstrate this through a "universal" spectrum of the Matrix Product State transfer matrix.

Refs.
A. Ueda and M. O., Phys. Rev. B 104, 165132 (2021); Phys. Rev. B 108, 024413 (2023).
J. T. Schneider, A. Ueda, Y. Liu, A. M. Läuchli, M. O., and L. Tagliacozzo, SciPost Phys. 18, 142 (2025).

 

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