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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…
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
Multi-messenger astronomy provides us with the possibility of discovering phenomenological signatures of quantum-gravity effects. This should be of paramount importance in the pursuit of an elusive quantum theory for the gravitational…
The size of Cooper pairs defines a fundamental length scale of superconductivity, conventionally set by band dispersion and the superconducting gap. This picture breaks down in flat bands, where quenched dispersion makes quantum geometry…
Classical methods of differential geometry are used to construct equations of motion for particles in quantum, electrodynamic and gravitational fields. For a five dimensional geometrical system, the equivalence principle can be extended.…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
For pure states, the quantum Berry curvature was well studied. However, the quantum curvature for mixed states has received less attention. From the concept of symmetric logarithmic derivative, we introduce a mixed-state quantum curvature…
We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space.…
As a fundamental concept in condensed matter physics, quantum geometry within the Riemannian metric elucidates various exotic phenomena, including the Hall effects driven by Berry curvature and quantum metric. In this work, we propose novel…
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…
Quantum geometry, describing the geometric properties of the Bloch wave function in momentum space, has recently been recognized as a fundamental concept in condensed matter physics. The flat-band system offers the paradigmatic platform…
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 concept of quantum geometry for single-particle states has revolutionized our interpretation of several emergent properties in condensed matter. However, a description of the quantum geometry for interacting particles and an…
The geometric structure of quantum states plays a fundamental role in determining the intrinsic dynamics of electrons in solids. In this work, we study the geometric origin of orbital angular momentum and its transport in a general two-band…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Optoelectronic and nonlinear transport experiments probe the quantum geometric tensor of Bloch states, whose real and imaginary components -- the quantum metric and the Berry curvature -- are typically constrained by symmetry. Here, we show…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static)…
Quantum geometry, a quantum mechanical quantity comprised of Berry curvature and quantum metric, describes the geometric structure of the electronic bands in solids. The correlation between nontrivial quantum geometry and quantum materials…
We develop a unified framework to compute band-geometric quantities in multiband systems whose low-energy Hamiltonians realize arbitrary $SU(2)$ representations. Exploiting the presence of a quantization axis, we use the Wigner--Eckart…