dorsal/arxiv
View SchemaIs efficiency of classical simulations of quantum dynamics related to integrability?
| Authors | Tomaz Prosen, Marko Znidaric |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608057 |
| URL | https://arxiv.org/abs/quant-ph/0608057 |
| DOI | 10.1103/PhysRevE.75.015202 |
| Journal | Phys.Rev.E 75, 015202 (2007) |
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_\epsilon(t), such that evolution of a long chain is accurate within fidelity error \epsilon up to time t. We find that rank generally increases exponentially, D_\epsilon(t) \propto \exp(const t), unless the system is integrable in which case we find polynomial increase.
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"abstract": "Efficiency of time-evolution of quantum observables, and thermal states of\nquenched hamiltonians, is studied using time-dependent density matrix\nrenormalization group method in a family of generic quantum spin chains which\nundergo a transition from integrable to non-integrable - quantum chaotic case\nas control parameters are varied. Quantum states (observables) are represented\nin terms of matrix-product-operators with rank D_\\epsilon(t), such that\nevolution of a long chain is accurate within fidelity error \\epsilon up to time\nt. We find that rank generally increases exponentially, D_\\epsilon(t) \\propto\n\\exp(const t), unless the system is integrable in which case we find polynomial\nincrease.",
"arxiv_id": "quant-ph/0608057",
"authors": [
"Tomaz Prosen",
"Marko Znidaric"
],
"categories": [
"quant-ph",
"cond-mat.other",
"nlin.SI"
],
"doi": "10.1103/PhysRevE.75.015202",
"journal_ref": "Phys.Rev.E 75, 015202 (2007)",
"title": "Is efficiency of classical simulations of quantum dynamics related to integrability?",
"url": "https://arxiv.org/abs/quant-ph/0608057"
},
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