A Spin Chain With Spiral Orders: Perspectives of Quantum Information and Mechanical Response

Gu, Shi-Jian; Yu, Wing Yiu; Lin, Hai‐Qing

doi:10.1142/s0217979213501063

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…In the case of two equal mixed states, the operator F has a set of eigenvalues, f n = Λ n , such that − ln Λ n reduces to the entanglement spectrum. The fidelity spectrum was studied in the cases of the XX spin chain in a magnetic field, a magnetic impurity inserted in a conventional superconductor and a bulk superconductor at finite temperature [153,154]. The information provided by the fidelity spectrum on the dominant modes that contribute to the distinguishability of phases forms parallels with the extra information provided by the entanglement spectrum [10] on the modes of a single phase compared to the von Neumann entropy.…”

Section: Fidelity Spectrummentioning

confidence: 99%

Entanglement and Fidelity: Statics and Dynamics

Sacramento

2023

Symmetry

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Herein, aspects of entanglement and fidelity and their use in condensed matter systems are briefly reviewed. Both static and time-dependent situations are considered. Different signatures of phases and phase transitions are discussed, including the dynamic aspects of the evolution across a critical point. Some emphasis is placed on the use of entanglement in phase transitions with no clear order parameters and no symmetry breaking.

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Section: Fidelity Spectrummentioning

confidence: 99%

Entanglement and Fidelity: Statics and Dynamics

Sacramento

2023

Symmetry

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“…Traditionally one compares states that differ infinitesimally due to some change of parameters of the Hamiltonian or due to some change in temperature or other intensive quantities associated with some reservoirs. The results together with some generalization, such as partial state fidelity 3,4 or the fidelity spectrum 5,6 , have been used to detect quantum phase transitions including those of a topological nature. This includes topological insulators and topological superconductors [7][8][9][10] .…”

Section: Introductionmentioning

confidence: 99%

Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence

2019

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The fidelity between two infinitesimally close states or the fidelity susceptibility of a system are known to detect quantum phase transitions. Here we show that the k-space fidelity between two states far from each other and taken deep inside (bulk) of two phases, generically vanishes at the k-points where there are gapless points in the energy spectrum that give origin to the lines (edges) separating the phases in the phase diagram. We consider a general case of two-band models and present a sufficient condition for the existence of gapless points, given there are pairs of parameter points for which the fidelity between the corresponding states is zero. By presenting an explicit counter-example, we showed that the sufficient condition is not necessary. Further, we showed that, unless the set of parameter points is suitably constrained, the existence of gapless points generically imply the accompanied pairs of parameter points with vanishing fidelity. Also, we showed the connection between the vanishing fidelity and gapless points on a number of concrete examples (topological triplet superconductor, topological insulator, 1d Kitaev model of spinless fermions, BCS superconductor, Ising model in a transverse field, graphene and Haldane Chern insulator), as well as for the more general case of Dirac-like Hamiltonians. We also briefly discuss the relation between the vanishing fidelity and gapless points at finite temperatures.

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“…With the motivation to gain more insight about a quantum phase from the fidelity approach, we proposed the fidelity spectrum in this work. Recently, Gu et al [21] and Sacramento et al [22] also introduced the concepts of mode fidelity and fidelity spectrum, respectively, with similar motivations.…”

Section: Introductionmentioning

confidence: 99%

Fidelity spectrum: A tool to probe the property of a quantum phase

2016

Chinese Phys. B

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Fidelity measures the similarity between two states and is widely adapted by the condensed matter community as a probe of quantum phase transitions in many-body systems. Despite its success in witnessing quantum critical points, information about the fine structure of a quantum phase one can get from this approach is still limited. Here, we proposed a scheme called fidelity spectrum. By studying the fidelity spectrum, one can obtain information about the characteristics of a phase. In particular, we investigated the spectra in the one-dimensional transverse-field Ising model and the twodimensional Kitaev model on a honeycomb lattice. It was found that the spectra have qualitative differences in the critical and non-critical regions of the two models. From the distributions of them, the dominating k modes in a particular phase could also be captured.

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A Spin Chain With Spiral Orders: Perspectives of Quantum Information and Mechanical Response

Cited by 4 publications

References 26 publications

Entanglement and Fidelity: Statics and Dynamics

Entanglement and Fidelity: Statics and Dynamics

Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence

Fidelity spectrum: A tool to probe the property of a quantum phase

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