paper

Universal Error Bound for Constrained Quantum Dynamics

arXiv:2001.03419 · doi:10.1103/PhysRevLett.124.210606

Abstract

It is well known in quantum mechanics that a large energy gap between a Hilbert subspace of specific interest and the remainder of the spectrum can suppress transitions from the quantum states inside the subspace to those outside due to additional couplings that mix these states, and thus approximately lead to a constrained dynamics within the subspace. While this statement has widely been used to approximate quantum dynamics in various contexts, a general and quantitative justification stays lacking. Here we establish an observable-based error bound for such a constrained-dynamics approximation in generic gapped quantum systems. This universal bound is a linear function of time that only involves the energy gap and coupling strength, provided that the latter is much smaller than the former. We demonstrate that either the intercept or the slope in the bound is asymptotically saturable by simple models. We generalize the result to quantum many-body systems with local interactions, for which the coupling strength diverges in the thermodynamic limit while the error is found to grow no faster than a power law in dimensions. Our work establishes a universal and rigorous result concerning nonequilibrium quantum dynamics.

arXiv comment5 pages, 3 figures. Accompanying paper arXiv:2001.03421. Here, we prove the asymptotic bound and provide general ideas for the many-body generalization, which is numerically demonstrated

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