Anatomy of 2D classical lattice models with TNR

Atsushi Ueda (ISSP, U of Tokyo)

Sep 16. 2022, 11:45 — 12:30

One of the most important but challenging tasks is constructing an effective field theory from a given lattice model. When the model is the 2D critical model, the effective theory is beautifully written by conformal field theory(CFT), allowing us to access the operator contents and their scaling dimensions. ZC. Gu showed that we could obtain this CFT information by the fixed point tensor of tensor network renormalization(TNR.)[1]

  However, the fixed point tensor does not exist at criticality due to the correlation upper bound induced by the finite bond dimension. As this error becomes crucial when the central charge is large, we only have reliable information from finite-size tensors.

  In this talk, based on our previous study[2], I will demonstrate how to construct an effective theory from a given lattice model in the vicinity of criticality. This method enables TNR to find the precise transition temperature, the operator contents and their OPE, and the RG flow of the theory.

  As a demonstration, I apply it to known models(Ising, Potts, XY) and unknown models(Regular polyhedron models[3]).

[1] ZC.Gu and XG, Wen Phys. Rev. B 80, 155131(2009)

[2] A.Ueda and M. Oshikawa, Phys. Rev. B 104, 165132(2021)

[3] H. Ueda et al. Phys. Rev. E 102, 032130(2020)


Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Tensor Networks: Mathematical Structures and Novel Algorithms (Thematic Programme)
Frank Pollmann (TU Munich)
Norbert Schuch (U of Vienna)
Frank Verstraete (Ghent U)