Is the efficiency of classical simulations of quantum dynamics related to integrability?
- 11 January 2007
- journal article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 75 (1), 015202
- https://doi.org/10.1103/physreve.75.015202
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.Comment: 4 pages; v2. added paragraph discussing pure stateKeywords
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This publication has 12 references indexed in Scilit:
- Efficient Approximation of the Dynamics of One-Dimensional Quantum Spin SystemsPhysical Review Letters, 2006
- Finite-temperature density matrix renormalization using an enlarged Hilbert spacePhysical Review B, 2005
- Real-time dynamics in spin-chains with adaptive time-dependent density matrix renormalization groupPhysical Review E, 2005
- Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative SystemsPhysical Review Letters, 2004
- Mixed-State Dynamics in One-Dimensional Quantum Lattice Systems: A Time-Dependent Superoperator Renormalization AlgorithmPhysical Review Letters, 2004
- Real-Time Evolution Using the Density Matrix Renormalization GroupPhysical Review Letters, 2004
- Efficient Simulation of One-Dimensional Quantum Many-Body SystemsPhysical Review Letters, 2004
- Quench dynamics across quantum critical pointsPhysical Review A, 2004
- Efficient Classical Simulation of Slightly Entangled Quantum ComputationsPhysical Review Letters, 2003
- Exact results for the dynamics of one-dimensional spin-systemsZeitschrift für Physik B Condensed Matter, 1976