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Connecting Entanglement in Time and Space: Improving the Folding Algorithm
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Connecting Entanglement in Time and Space: Improving the Folding Algorithm
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The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the temporal entanglement. We show that this temporal entanglement is, in many cases, equal to the spatial entanglement of a modified Hamiltonian. This inspires a modification to the folding algorithm, that we call the "hybrid algorithm". We find that this leads to improved accuracy for the same numerical effort. We then use these algorithms to study relaxation in a transverse plus parallel field Ising model, finding persistent quasi-periodic oscillations for certain choices of initial conditions.
Forward citations
Cited by 3 Pith papers
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Temporal Entanglement from Twist Correlators in 2d Conformal Field Theory and Holography
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Extracting conformal data from Loschmidt echoes after critical quenches
Boundary-CFT scaling dimensions and central charge can be reconstructed from the system-size dependence and phase of Loschmidt echoes after a critical quench, bypassing ground-state preparation.
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Mesoscopic Regimes of Temporal Entanglement in Ergodic Quantum Systems
Generic ergodic Hamiltonian dynamics in quantum Ising chains exhibits a long mesoscopic regime in temporal entanglement that deviates from random-circuit universality, suggesting slow spectral reorganization of the in...
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