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

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.

4 pages; v2. added paragraph discussing pure states

References in corpus (4)

• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quench dynamics across quantum critical points
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently

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• Complexity of thermal states in quantum spin chains
• Entanglement of random vectors
• Optimal two-qubit gate for generation of random bipartite entanglement
• Initial-state randomness as a universal source of decoherence