Lieb-Robinson bounds on the speed of information propagation

Isabeau Prémont-Schwarz and Jeff Hnybida
Phys. Rev. A 81, 062107 – Published 9 June 2010

Abstract

We propose Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found that the Lieb-Robinson speed is not always algebraic in the interaction strengths. We consider Hamiltonians with any finite number of bounded operators and also a certain class of unbounded operators. We obtain bounds and propagation speeds for quantum systems on lattices and also general graphs possessing a kind of homogeneity and isotropy. One area for which this formalism could be useful is the study of quantum phase transitions which occur when interactions strengths are varied.

  • Figure
  • Received 22 February 2010

DOI:https://doi.org/10.1103/PhysRevA.81.062107

©2010 American Physical Society

Authors & Affiliations

Isabeau Prémont-Schwarz* and Jeff Hnybida

  • Perimeter Institute for Theoretical Physics 31 Caroline Street N, Waterloo, Ontario N2L 2Y5, Canada
  • Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

  • *ipremont-schwarz@perimeterinstitute.ca
  • jhnybida@perimeterinstitute.ca

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Issue

Vol. 81, Iss. 6 — June 2010

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