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Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Nov;90(5-1):052103. Epub 2014 Nov 4.

Mixed-state fidelity susceptibility through iterated commutator series expansion.

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Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee Boulevard, 1784 Sofia, Bulgaria.


We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provide an analytical expression for the MFS as a formal expansion in terms of the thermodynamic mean values of successively higher commutators of the Hamiltonian with the operator involved through the control parameter. That expression is naturally divided into two parts: the usual isothermal susceptibility and a constituent in the form of an infinite series of thermodynamic mean values which encodes the noncommutativity in the problem. If the symmetry properties of the Hamiltonian are given in terms of the generators of some (finite-dimensional) algebra, the obtained expansion may be evaluated in a closed form. This issue is tested on several popular models, for which it is shown that the calculations are much simpler if they are based on the properties from the representation theory of the Heisenberg or SU(1, 1) Lie algebra.


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