Universal Error Bound for Constrained Quantum Dynamics
- URL: http://arxiv.org/abs/2001.03419v4
- Date: Sat, 2 May 2020 07:37:30 GMT
- Title: Universal Error Bound for Constrained Quantum Dynamics
- Authors: Zongping Gong, Nobuyuki Yoshioka, Naoyuki Shibata, Ryusuke Hamazaki
- Abstract summary: We establish an observable-based error bound for a constrained-dynamics approximation in generic gapped quantum systems.
Our work establishes a universal and rigorous result concerning nonequilibrium quantum dynamics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 $t^{d+1}$ in $d$ dimensions. Our work establishes a universal
and rigorous result concerning nonequilibrium quantum dynamics.
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