The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned...The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned only for pure states,has limited applicability in realistic scenarios where mixed states are common.To address this limitation,we generalize the defnition of the QGT to mixed states using the purifcation bundle and the covariant derivative.Notably,our proposed defnition reduces to the traditional QGT when mixed states approach pure states.In our framework,the real and imaginary parts of this generalized QGT correspond to the Bures metric and the mean gauge curvature,respectively,endowing it with a broad range of potential applications.Additionally,using our proposed mixed-state QGT,we derive the geodesic equation applicable to mixed states.This work establishes a unifed framework for the geometric analysis of both pure and mixed states,thereby deepening our understanding of the geometric properties of quantum states.展开更多
The kagome lattice,characterized by its network of cornersharing triangles,provides an excellent platform for studying various novel quantum phenomena.The recently discovered kagome metal AV3Sb5(A=K,Rb,Cs)[1]garners s...The kagome lattice,characterized by its network of cornersharing triangles,provides an excellent platform for studying various novel quantum phenomena.The recently discovered kagome metal AV3Sb5(A=K,Rb,Cs)[1]garners significant attention for its unique properties,including an unconventional charge density wave(CDW)and superconductivity(SC)[2],as well as the interplay between CDW and SC[3].展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12347104,U24A2017,12461160276,and 12175075)the National Key Research and Development Program of China(Grant No.2023YFC2205802)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant Nos.BK20243060 and BK20233001)in part by the State Key Laboratory of Advanced Optical Communication Systems and Networks,China。
文摘The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned only for pure states,has limited applicability in realistic scenarios where mixed states are common.To address this limitation,we generalize the defnition of the QGT to mixed states using the purifcation bundle and the covariant derivative.Notably,our proposed defnition reduces to the traditional QGT when mixed states approach pure states.In our framework,the real and imaginary parts of this generalized QGT correspond to the Bures metric and the mean gauge curvature,respectively,endowing it with a broad range of potential applications.Additionally,using our proposed mixed-state QGT,we derive the geodesic equation applicable to mixed states.This work establishes a unifed framework for the geometric analysis of both pure and mixed states,thereby deepening our understanding of the geometric properties of quantum states.
基金support from the National Key R&D Program of China(2021YFA1401800 and 2021YFA1400202)the National Natural Science Foundation of China(12141404)+7 种基金the Natural Science Foundation of Shanghai(22ZR1479700 and 23XD1422200)Shaofeng Duan acknowledged support from the China Postdoctoral Science Foundation(2022M722108)the China National Postdoctoral Program for Innovative Talents(BX20230216)the National Natural Science Foundation of China(12304178)Yanfeng Guo acknowledged the National Key R&D Program of China(2023YFA1406100)the Double First-Class Initiative Fund of ShanghaiTech Universitysupport from the National Key R&D Program of China(2022YFA1402400 and 2021YFA1400100)the National Natural Science Foundation of China(12074248).
文摘The kagome lattice,characterized by its network of cornersharing triangles,provides an excellent platform for studying various novel quantum phenomena.The recently discovered kagome metal AV3Sb5(A=K,Rb,Cs)[1]garners significant attention for its unique properties,including an unconventional charge density wave(CDW)and superconductivity(SC)[2],as well as the interplay between CDW and SC[3].
