Time Scale for Adiabaticity Breakdown in Driven Many-Body Systems and Orthogonality Catastrophe

Oleg Lychkovskiy, Oleksandr Gamayun, Vadim Cheianov

    Research output: Contribution to journalArticlepeer-review

    26 Citations (Scopus)

    Abstract

    The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely, many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter-dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving nonautonomous time evolution in a large Hilbert space.

    Original languageEnglish
    Article number200401
    JournalPhysical Review Letters
    Volume119
    Issue number20
    DOIs
    Publication statusPublished - 13 Nov 2017

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