Related papers: Quantum Geometry in Quantum Materials
Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike the…
The quantum geometry of Bloch wavefunctions underpins a wealth of emergent phenomena in quantum materials. Its imaginary part, the Berry curvature, has long been recognized as a key source for hallmark effects such as quantum Hall and…
The exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the…
Quantum geometry has been identified as an important ingredient for the physics of quantum materials and especially of flat-band systems, such as moir\'e materials. On the other hand, the coupling between light and matter is of key…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
Bloch electrons in multiorbital systems carry quantum geometric information characteristic of their wavevector-dependent interorbital mixing. The geometric nature impacts electromagnetic responses, and this effect carries over to the…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Bloch wave functions of electrons have properties called quantum geometry, which has recently attracted much attention as the origin of intriguing physical phenomena. In this paper, we introduce the notion of the quantum-geometric pair…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
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 local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states…
This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting…