Lower and upper bounds on the fidelity susceptibility

Jg, Brankov; Ns, Tonchev

doi:10.1103/physreve.85.031115

Cited by 5 publications

(19 citation statements)

References 37 publications

(68 reference statements)

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“…To avoid confusion, we warn the reader that MFS χ F (ρ) differs from the MFS χ G F (ρ) derived in [14] by extending the ground-state Green's function representation to nonzero temperatures, although in the pure states both definitions coincide. This fact has been pointed out in [24], see also the discussion in [15] and [16,25].…”

Section: Spectral Representation Of the Mfsmentioning

confidence: 55%

“…The main computational obstacles in obtaining χ F (ρ) arise in the non commutative case of the Hamiltonian (4). To proceed with the calculations in the case when the operators T and S do not commute, we make use of the convenient spectral representation introduced in [15]. We assume that the Hermitian operator T has a complete orthonormal set of eigenvectors |n , T |n = T n |n , where n = 1, 2, .…”

Section: Spectral Representation Of the Mfsmentioning

confidence: 99%

“…The relationship (6) explains why the terms Bures metric and MFS are used interchangeably in the literature (see, e.g., [13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

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Mixed-state fidelity susceptibility through iterated commutator series expansion

2014

Phys. Rev. E

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We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provides 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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Section: Spectral Representation Of the Mfsmentioning

confidence: 55%

Section: Spectral Representation Of the Mfsmentioning

confidence: 99%

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Mixed-state fidelity susceptibility through iterated commutator series expansion

2014

Phys. Rev. E

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“…Some applications of these functionals have been demonstrated in [35,37,38]. Since F 0 (S; S) = (S; S) T hereafter in the text we shall use this notation for the Bogoliubov-Duhamel inner product.…”

Section: Appendix: the Bogoliobov-duhamel Inner Product Moments Of Tmentioning

confidence: 99%

“…[6,10,[36][37][38] and references therein. The Bures metric d 2 B appears under different names: quantum Fisher information (apart from a numerical factor), SLD metric, fidelity susceptibility, etc [4,6,18,19].…”

Section: Introductionmentioning

confidence: 99%

Monotone Riemannian metrics and dynamic structure factor in condensed matter physics

Tonchev

2016

Journal of Mathematical Physics

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An analytical approach is developed to the problem of computation of monotone Riemannian metrics (e.g. Bogoliubov-Kubo-Mori, Bures, Chernoff, etc.) on the set of quantum states. The obtained expressions originate from the Morozova,Cencov and Petz correspondence of monotone metrics to operator monotone functions. The used mathematical technique provides analytical expansions in terms of the thermodynamic mean values of iterated (nested) commutators of a model Hamiltonian T with the operator S involved through the control parameter h. Due to the sum rules for the frequency moments of the dynamic structure factor new presentations for the monotone Riemannian metrics are obtained. Particularly, relations between any monotone Riemannian metric and the usual thermodynamic susceptibility or the variance of the operator S are discussed. If the symmetry properties of the Hamiltonian are given in terms of generators of some Lie algebra, the obtained expansions may be evaluated in a closed form. These issues are tested on a class of model systems studied in condensed matter physics.2

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Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction

et al. 2017

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Lower and upper bounds on the fidelity susceptibility

Cited by 5 publications

References 37 publications

Mixed-state fidelity susceptibility through iterated commutator series expansion

Mixed-state fidelity susceptibility through iterated commutator series expansion

Monotone Riemannian metrics and dynamic structure factor in condensed matter physics

Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction

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