A Lanczos approach to the Adiabatic Gauge Potential

• URL: http://arxiv.org/abs/2302.07228v1
• Date: Tue, 14 Feb 2023 18:18:21 GMT
• Title: A Lanczos approach to the Adiabatic Gauge Potential
• Authors: Budhaditya Bhattacharjee
• Abstract summary: The Adiabatic Gauge Potential (AGP) measures the rate at which the eigensystem of Hamiltonian changes under adiabatic deformations. We employ a version of this approach by using the Lanczos algorithm to evaluate the AGP operator in terms of Krylov vectors and the AGP norm in terms of the Lanczos coefficients.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Adiabatic Gauge Potential (AGP) measures the rate at which the eigensystem of Hamiltonian changes under adiabatic deformations. There are many ways of constructing the AGP operator and evaluating the AGP norm. Recently, it was proposed that a Gram-Schmidt-type algorithm can be used to explicitly evaluate the expression of the AGP. We employ a version of this approach by using the Lanczos algorithm to evaluate the AGP operator in terms of Krylov vectors and the AGP norm in terms of the Lanczos coefficients. The algorithm is used to explicitly construct the AGP operator for some simple systems. We derive a relation between the AGP norm and the autocorrelation function of the deformation operator. We present a modification of the variational approach to derive the regulated AGP norm with the least number of computational steps. Using this, we approximate the AGP to varying degrees of success. Finally, we compare and contrast the quantum chaos probing capacities of the AGP and K-complexity, in view of the Operator Growth Hypothesis.

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