Local scale transformations on the lattice with tensor network renormalization

Abstract

Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization (TNR) algorithm [\emph{G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405}] can be used to implement local scale transformations on these objects, namely a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.

Revised version, with additional numeric results. Main text: 5 pages, 5 figures. Supplementary material: 9 pages, 13 figures

References in corpus (4)

• A class of quantum many-body states that can be efficiently simulated
• Tensor renormalization group approach to 2D classical lattice models
• Algorithms for tensor network renormalization
• Topological conformal defects with tensor networks

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