Related papers: Berry Curvature and Riemann Curvature in Kinematic…
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…
The band geometric properties of quantum materials play an elemental role in the linear and nonlinear transport of electrons. In this paper, we propose that the interplay of the Berry curvature, the orbital magnetic moment and the Lorentz…
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…
Magnetic semimetals have increasingly emerged as lucrative platforms hosting spin-based topological phenomena in real and momentum spaces. Of particular interest is the emergence of Berry curvature, whose geometric origin, accessibility…
For a long period of time, we have been seeking how Berry curvature influnces the transport properties in materials breaking time-reversal symmetry. In time-reversal symmetric material, there will be no thermoelectric current induced by…
We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space -- the natural setting for describing conformal field theories in two fewer…
Exploring the topological characteristics of electronic bands is essential in condensed matter physics. Moir\'e materials featuring flat bands provide a versatile platform for engineering band topology and correlation effects. In moir\'e…
In this paper, we find the boundary dual of the symplectic form for the bulk fields in any entanglement wedge. The key ingredient is Uhlmann holonomy, which is a notion of parallel transport of purifications of density matrices based on a…
The Berry curvature plays a key role in the magnetic transport of topological materials. Yet, it is not clear whether the Berry curvature by itself can give rise to universal transport phenomena with specific scaling behaviors. In this…
The paper aims to spell out the relevance of the Berry phase in view of the question what the minimal mathematical structure is that accounts for all observable quantum phenomena. The question is both of conceptual and of ontological…
An extension of the Hellmann-Feynman theorem to one employing dynamical parameters that vary with time according to quantum dynamics is rigorously derived, avoiding any linear response or other approximations. The resulting theorem for the…
Riemannian geometry is a particular case of Hamiltonian mechanics: the orbits of the hamiltonian $H=\frac{1}{2}g^{ij}p_{i}p_{j}$ are the geodesics. Given a symplectic manifold (\Gamma,\omega), a hamiltonian $H:\Gamma\to\mathbb{R}$ and a…
A three-dimensional non-Hermitian Hamiltonian with parity-time symmetry can exhibit a closed exceptional surface (EP surface) in momentum space, which is a non-Hermitian deformation of the degeneracy line (DL). Since the degeneracy line…
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…
We explore the interplay between Berry curvature and topological properties in single-flavor color superconductors, where quarks form spin-one Cooper pairs. By deriving a new relation, we connect the topological nodal structure of the gap…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
A kinetic theory can be modified to incorporate triangle anomalies and the chiral magnetic effect by taking into account the Berry curvature flux through the Fermi surface. We show how such a kinetic theory can be derived from underlying…
Berry curvature does not show itself in the relative phase correlation of wave-functions at different spatial points in a metal unless the fermions have closed trajectories in momentum space, for example those around isolated impurities.…
A family of finite-dimensional quantum systems with a non-degenerate ground state gives rise to a closed 2-form on the parameter space: the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. We…
It has been recently established that optoelectronic and non-linear transport experiments can give direct access to the dipole moment of the Berry curvature in non-magnetic and non-centrosymmetric materials. Thus far, non-vanishing Berry…