Conformal Fields and Operator Product Expansion in Critical Quantum Spin Chains

Yijian Zou, Ashley Milsted, and Guifre Vidal
Phys. Rev. Lett. 124, 040604 – Published 28 January 2020
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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 ϕα of the corresponding primary CFT operators ϕαCFT. We then show how to numerically compute the operator product expansion coefficients CαβγCFT 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.

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  • Received 24 September 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.040604

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yijian Zou1,2,*, Ashley Milsted1, and Guifre Vidal1

  • 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
  • 2University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

  • *yzou@pitp.ca

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Vol. 124, Iss. 4 — 31 January 2020

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