Abstract
At a quantum critical point, the low-energy physics of a quantum spin chain is described by conformal field theory (CFT). Given the Hamiltonian of a critical spin chain, we propose a variational method to build an approximate lattice representation of the corresponding primary CFT operators . We then show how to numerically compute the operator product expansion coefficients governing the fusion of two primary fields. In this way, we complete the implementation of Cardy’s program, outlined in the 1980s, which aims to extract the universality class of a phase transition, as encoded in the so-called conformal data of the underlying CFT, starting from a microscopic description. Our approach, demonstrated here for the critical quantum Ising model, only requires a generic (i.e., in general, nonintegrable) critical lattice Hamiltonian as its input.
- Received 24 September 2019
DOI:https://doi.org/10.1103/PhysRevLett.124.040604
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