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

Tomaz Prosen·Marko Znidaric
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Abstract

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 non-integrable - quantum chaotic case as control parameters are varied. Quantum states (observables) are represented in terms of matrix-product-operators with rank D_ε(t), such that evolution of a long chain is accurate within fidelity error εup to time t. We find that rank generally increases exponentially, D_ε(t) \propto \exp(const t), unless the system is integrable in which case we find polynomial increase.

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Tomaz Prosen, Marko Znidaric. 2006-09-14. Is efficiency of classical simulations of quantum dynamics related to integrability?. https://doi.org/10.1103/physreve.75.015202

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