A global adiabatic criterion selects Gaussian pulse timings that suppress leakage during non-Abelian Thouless pumping in a twelve-level Rydberg synthetic Lieb lattice, yielding order-dependent population transport consistent with noncommuting holonomic operations.
Simon, Holonomy, the quantum adiabatic theorem, and Berry’s phase, Phys
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Extending the wave-packet ansatz for Bloch electrons to include interband contributions and applying the time-dependent variational principle yields leading-order nonadiabatic corrections to the Lagrangian, including an energy-gap-renormalized quantum metric that recasts dynamics as geodesic motion.
For pseudo-Hermitian systems the norm-preserving Berry connection is the Hermitian one obtained via the Hilbert-space metric; the standard biorthogonal connection mixes eigenspace geometry with metric artifacts, and can vanish where the conventional one is nonzero.
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Non-Abelian Thouless pumping based on the global adiabatic criterion in Rydberg synthetic lattices
A global adiabatic criterion selects Gaussian pulse timings that suppress leakage during non-Abelian Thouless pumping in a twelve-level Rydberg synthetic Lieb lattice, yielding order-dependent population transport consistent with noncommuting holonomic operations.
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Nonadiabatic Wave-Packet Dynamics: Nonadiabatic Metric, Quantum Geometry, and Gravitational Analogy
Extending the wave-packet ansatz for Bloch electrons to include interband contributions and applying the time-dependent variational principle yields leading-order nonadiabatic corrections to the Lagrangian, including an energy-gap-renormalized quantum metric that recasts dynamics as geodesic motion.
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Covariant formulation of the Berry connection in non-Hermitian systems
For pseudo-Hermitian systems the norm-preserving Berry connection is the Hermitian one obtained via the Hilbert-space metric; the standard biorthogonal connection mixes eigenspace geometry with metric artifacts, and can vanish where the conventional one is nonzero.