A diagonalization-free Krylov (bi-Lanczos/Arnoldi) construction yields exact or truncated adiabatic gauge potentials for non-Hermitian STA, reducing them to sparse matrix equations that suppress nonadiabatic excitations and detect PT/EP transitions.
Universal defect statistics in counterdiabatic quantum critical dynamics
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abstract
Counterdiabatic driving (CD) provides a framework for suppressing excitations in nonadiabatic processes. Exact CD protocols require nonlocal control fields, and CD approximations with tailored locality are needed for their implementation. However, the performance of local CD schemes remains poorly understood. Here, we develop an analytically tractable local CD expansion scheme and establish a universal scaling theory governing the defect statistics after crossing a quantum phase transition as a function of the CD locality order. Our predictions are tested on the transverse field Ising model and long-range Kitaev models. Our results provide an analytical framework for evaluating the effectiveness of local CD protocols in quantum state preparation, control, and optimization.
fields
quant-ph 3representative citing papers
The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturates only when the Hamiltonian commutes with itself at different times.
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic states and supersymmetric systems.
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Shortcuts to Adiabaticity for non-Hermitian systems in Krylov Space
A diagonalization-free Krylov (bi-Lanczos/Arnoldi) construction yields exact or truncated adiabatic gauge potentials for non-Hermitian STA, reducing them to sparse matrix equations that suppress nonadiabatic excitations and detect PT/EP transitions.
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Krylov Dynamics and Operator Growth in Time-Dependent Systems via Lie Algebras
The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturates only when the Hamiltonian commutes with itself at different times.
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Krylov Complexity Under Hamiltonian Deformations and Toda Flows
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic states and supersymmetric systems.