Related papers: Quantum Geometry Phenomena in Condensed Matter Sys…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We investigate the post-quench dynamics of the quantum geometric tensor (QGT) of 1D periodic systems with a suddenly changed Hamiltonian. The diagonal component with respect to the crystal momentum gives a metric corresponding to the…
We study characteristics of quantum evolution which can be called curvature and torsion. The curvature shows a deviation of the state vector in quantum evolution from the geodesic line. The torsion shows a deviation of state vector from the…
In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the…
We show that Hall viscosity in lattice bands is governed by a band-projected electric quadrupole encoded within the quantum geometry: Berry curvature sets the projected-coordinate algebra, while the quantum metric determines the quadrupolar…
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…
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum…
We take as a starting point an expression for the quantum geometric tensor recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of…
Ideal Chern insulating phases arise in two-dimensional systems with broken time-reversal symmetry. They are characterized by having nearly-flat bands, and a uniform quantum geometry -- which combines the Berry curvature and quantum metric…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…
We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field…
The quantum geometric tensor (QGT) of a quantum system in a given parameter space captures both the geometry of the state manifold and the topology of the system. While the local QGT elements have been successfully measured in various…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly.…
Electrical current fluctuations provide a powerful and unconventional probe of band geometry in quantum materials. In particular, intrinsic noise components that are independent of the relaxation time reveal universal band-geometric…
Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of…
The quantum geometric tensor (QGT) characterizes the complete geometric properties of quantum states, with the symmetric part being the quantum metric, and the antisymmetric part being the Berry curvature. We propose a generic Hamiltonian…
Coherent quantum phenomena can only emerge when decoherence is minimized, and mastery over decoherence is technologically crucial for designing and operating functional quantum devices. However, its microscopic mechanisms in…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
Recently, it has been shown that a quantum system held in spatial superposition and then eventually recombined does experience decoherence from black hole horizons, at a level increasing linearly with the time the superposition has been…