Perturbative power series for block diagonalisation of Hermitian matrices

• URL: http://arxiv.org/abs/2408.14637v1
• Date: Mon, 26 Aug 2024 21:05:26 GMT
• Title: Perturbative power series for block diagonalisation of Hermitian matrices
• Authors: Ishan N. H. Mankodi, David P. DiVincenzo,
• Abstract summary: We show that two conditions, least action" vs. block-off-diagonality of the generator, lead to identical transformations. We derive the perturbative power series of the least action", exhibiting explicitly the loss of block-off-diagnoality.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Block diagonalisation of matrices by canonical transformation is important in various fields of physics. Such diagonalization is currently of interest in condensed matter physics, for modelling of gates in superconducting circuits and for studying isolated quantum many-body systems. While the block diagonalisation of a particular Hermitian matrix is not unique, it can be made unique with certain auxiliary conditions. It has been assumed in some recent literature that two of these conditions, ``least action" vs. block-off-diagonality of the generator, lead to identical transformations. We show that this is not the case, and that these two approaches diverge at third order in the small parameter. We derive the perturbative power series of the ``least action", exhibiting explicitly the loss of block-off-diagnoality.

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