Mixed-state fidelity and quantum criticality at finite temperature

Zanardi, Paolo; Quan, H. T.; Wang, Xiaoguang; Sun, C. P.

doi:10.1103/physreva.75.032109

Cited by 204 publications

(195 citation statements)

References 16 publications

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“…All these results have been obtained in the zero temperature limit that we adopt in this work. Even though a consistent theory of fidelity in finite temperatures is still missing, several results have already been obtained [19][20][21]. This article is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Rams

Damski

2011

Phys. Rev. A

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We study ground state fidelity defined as the overlap between two ground states of the same quantum system obtained for slightly different values of the parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY model and the neighborhood of its critical points. We describe in detail cases when fidelity is dominated by the universal contribution reflecting quantum criticality of the phase transition. We show that proximity to the multicritical point leads to anomalous scaling of fidelity. We also discuss fidelity in a regime characterized by pronounced oscillations resulting from the change of either the system size or the parameters of the Hamiltonian. Moreover, we show when fidelity is dominated by non-universal contributions, study fidelity in the extended Ising model, and illustrate how our results provide additional insight into dynamics of quantum phase transitions. Special attention is put to studies of fidelity from the momentum space perspective. All our main results are obtained analytically. They are in excellent agreement with numerics.

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Section: Introductionmentioning

confidence: 99%

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Rams

Damski

2011

Phys. Rev. A

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“…In the last few years, there have been many studies of the phase diagrams for various quantum models in the aid of the fidelity [13][14][15][16][17][18][19] or mixed-state fidelity [2,[20][21][22]. All the investigations are performed for Hermitian Hamiltonians, where the probability is preserving in the context of standard Dirac inner product.…”

Section: Model and Solutionmentioning

confidence: 99%

“…It turns out that the mixedstate fidelity, which is related to the statistical distance between two density operators, is a powerful way to describe the signatures of QPTs at nonzero temperature [2].…”

Section: Introductionmentioning

confidence: 99%

Finite-temperature quantum criticality in a complex-parameter plane

Song

2015

Phys. Rev. A

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A conventional quantum phase transition (QPT) occurs not only at zero temperature, but also exhibits finite-temperature quantum criticality. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the finite-temperature quantum criticality in a non-Hermitian PT -symmetric Ising model. We present the complete set of exact eigenstates of the non-Hermitian Hamiltonian, based on which the mixed-state fidelity in the context of biorthogonal bases is calculated. Analytical and numerical results show that the fidelity approach to finite-temperature QPT can be extended to the non-Hermitian Ising model. This paves the way for experimental detection of quantum criticality in a complex-parameter plane.

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“…In recent decade different concepts emerging from quantum-information geometry [1][2][3][4] have been intensively incorporated in condensed matter physics [5][6][7][8][9][10][11][12][13][14][15][16][17]. The underlying idea may be briefly reviewed as follows.…”

Section: Introductionmentioning

confidence: 99%

“…The notion of distance has found applications in different fields. For example: thermodynamic of small systems [5,16], geometrical description of phase transitions and quantum criticality [6][7][8][9][10][11][12][13][14][15], quantum estimation of Hamiltonian parameters [18,19] and hypothesis testing and discrimination of states [20][21][22][23], are only a part of them. If we consider the distance between two states obtained by an infinitesimal change in the values of the parameters that specifie the quantum state, we come to the notion of a metric tensor, i.e.…”

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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Mixed-state fidelity and quantum criticality at finite temperature

Cited by 204 publications

References 16 publications

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Finite-temperature quantum criticality in a complex-parameter plane

Monotone Riemannian metrics and dynamic structure factor in condensed matter physics

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