Tensor network renormalization: scale invariance on the lattice


Guifre Vidal (Perimeter Institute for Theoretical Physics)


I will discuss how to define scale transformations on 1d quantum (or 2d classical) systems on the lattice. At a quantum (or thermal) critical point, one expects scale invariance in the continuum. On the lattice, however, scale invariance is explicitly broken by the lattice spacing. Nevertheless, we will see that one can still define global scale transformations on the lattice, under which the critical 1d ground state (2d partition function) is explicitly invariant and, more generally, an RG flow is produced with the correct structure of fixed points. Moreover, one can similarly define local scale transformations on the lattice, and observe an emergent local scale invariance/covariance. On the practical side, such transformations yield accurate numerical estimates of the universal data characterizing the phase transition --- namely the central charge, scaling dimensions, conformal spins, and operator product expansion coefficients of the underlying conformal field theory. Based on work with Glen Evenbly et al, arXiv:1412.0732, arXiv:1502.05385, arXiv:1510.00689, and arXiv:1510.07637.

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