Adiabatic Theorem for Quantum Spin Systems

S. Bachmann, W. De Roeck, and M. Fraas
Phys. Rev. Lett. 119, 060201 – Published 11 August 2017

Abstract

The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ϵ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo’s linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.

  • Figure
  • Received 6 December 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.060201

© 2017 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Bachmann1, W. De Roeck2, and M. Fraas2

  • 1Mathematisches Institut der Universität München, Munich 80333, Germany
  • 2Instituut voor Theoretische Fysica, KU Leuven, Leuven 8001, Belgium

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Issue

Vol. 119, Iss. 6 — 11 August 2017

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