Is the efficiency of classical simulations of quantum dynamics related to integrability?

Jan 11, 2007
Published in:
  • Phys.Rev.E 75 (2007) 1, 015202
  • Published: Jan 11, 2007

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Abstract: (APS)
Efficiency of time evolution of quantum observables, and thermal states of quenched Hamiltonians, is studied using time-dependent density-matrix renormalization group method in a family of generic quantum spin chains which undergo a transition from integrable to nonintegrable-quantum chaotic case as control parameters are varied. Quantum states (observables) are represented in terms of matrix-product operators with rank Dϵ(t){D}_{ϵ}(t), such that evolution of a long chain is accurate within fidelity error ϵϵ up to time tt. We found that the rank generally increases exponentially {D}_{ϵ}(t)\ensuremath{\propto}\mathrm{exp}(\mathrm{const}\phantom{\rule{0.2em}{0ex}}t), unless the model system was integrable in which case we found polynomial increase.