Fidelity approach to quantum phase transitions

By S. Gu. 2008

477 citations recorded by the source corpus.

We review the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin–Meshkov–Glick model, are introduced at the graduate-student level. Besides, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/46ff219d7f46950c48675abbae8a07528511c812

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Physical and Theoretical Chemistry

Citations in the corpus

Quantum-enhanced measurements without entanglement (2017, background): “Thus, the divergence or the superextensivity of the quantum Fisher Information reveals a quantum phase transition but the converse does not hold: see (Gu, 2010) for a review.”
Quantum Fisher information matrix and multiparameter estimation (2019, background): “In 2007, You et al. [18,108] first studied the connection between the fidelity susceptibility and the correlation function, and then in 2016, Hauke et al. [109] extended this connection between the QFI and the symmetric and asymmetric correlation functions to the thermal states.”
Band geometry, Berry curvature and superfluid weight (2016, background): “The quantum metric has found applications in the theory of quantum entanglement and quantum information [7] and can be used to detect quantum phase transitions [8].”
Non-Equilibrium Phase Transitions (2010, background): “Many equilibrium phase transitions are detected by superextensivity of the Bures metric, also known as fidelity susceptibility [4] and proportional to the Fisher information [5, 6].”
Quantum spin squeezing (2010, background): “Therefore, considering these intrinsic properties of QPTs, researchers investigated there by using concepts borrowed from quantum information [11,12], such as quantum entanglement [6,9] and fidelity [258].”
Geometry of quantum phase transitions (2019, methodology): “This provides the means to venture into the study of models where analytical solutions are not available [160, 204, 205, 207, 210, 211].”
Quantum Simulation of a Lattice Schwinger Model in a Chain of Trapped Ions (2013, methodology): “The assumption of two transitions is confirmed by the fidelity susceptibility, which is a reliable tool to detect conventional quantum phase transitions [80, 81].”