Related papers: The Quantum Geometric Tensor in a Parameter Depend…
Berry curvature fundamentally dictates the topological ground state, anomalous transport and optical properties of quantum materials. However, directly mapping its momentum-space distribution in real materials remains an outstanding…
Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the…
Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric…
We consider a massive quantum test Klein-Gordon field probing an isotropic quantum cosmological space-time in the background. The result obtained is surprising. It turns out, that despite the isotropy of the quantum gravitational field, the…
Quantum geometry of the electron wave function plays a significant role in the linear and non-linear responses of crystalline materials. Here, we study quantum geometry induced second harmonic generation. We identify non-linear responses…
The quantum metric, a key component of quantum geometry, plays a central role in a wide range of physical phenomena and has been extensively studied in periodic crystals and moir\'{e} materials. Here, we systematically investigate quantum…
We elaborate that $s$-wave and $d$-wave superconductors described by mean field theories possess a nontrivial quantum geometry. From the overlap of two quasihole states at slightly different momenta, one can define a quantum metric that…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
A three-dimensional anisotropic quantum well placed in an adiabatically precessing uniform magnetic field is considered and an explicit formula for the Berry phase is obtained. To get the Berry phase, a purely algebraic algorithm of…
We discover the connection between the Berry curvature and the Riemann curvature tensor in any kinematic space of minimal surfaces anchored on spherical entangling surfaces. This new holographic principle establishes the Riemann geometry in…
The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems,…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully…
In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT), whose imaginary part is the Berry curvature and real part is the quantum metric tensor. Here, we propose and experimentally implement a…
The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor which characterizes the topology of quantum states. The former is known to generate a zoo of important discoveries…
The quantum geometric tensor (QGT) provides nontrivial bounds among physical quantities, as exemplified by the metric-curvature inequality. In this paper, we investigate various bounds for different observables through certain…
Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In…
The second-order nonlinear current originates from three physical mechanisms: extrinsic nonlinear Drude and Berry curvature dipole and intrinsic Berry connection polarizability. Here, we predict a new intrinsic contribution to the current…