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Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components:…
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in…
Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the…
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc.…
The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
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…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators.…
Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most famously, local geometrical characteristics like the Berry curvature can…
Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is at the core of modern physics. The Quantum Geometric Tensor (QGT) is a central physical object in this regard, encoding…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
Geometric analogs of Bloch oscillations studied so far have relied on Berry curvature. We show that a weakly inhomogeneous electric field adds a distinct quantum-metric term to semiclassical wavepacket dynamics, generating an oscillatory…
The Berry curvature characterizes one aspect of the geometry of quantum states. It materializes, among other consequences, as an anomalous velocity of wave packets. In non-Hermitian systems, wave packet dynamics is enriched by additional…
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 materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of electronic wavefunctions, encoded in the quantum metric and Berry curvature. Whereas Berry curvature-mediated transport…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…