Related papers: Quantum Geometry and the Hidden Scales in Material…
We show that, quite generally, quantum geometry plays a major role in determining the low-energy physics in strongly correlated lattice models at fractional band fillings. We identify limits in which the Fubini Study metric dictates the…
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…
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…
Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy…
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…
Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure…
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…
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…
Quantum geometry of Bloch wavefunctions has gained considerable interest with the discovery of moir\'e materials that exhibit bands flattened by quantum interference. The quantum metric, the symmetric part of the quantum geometric tensor,…
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…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
The quantum geometric properties of a Bloch state in momentum space are usually described by the Berry curvature and quantum metric. In realistic gapped materials where interactions and disorder render the Bloch state not a viable starting…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
The geometric characteristics of Bloch wave functions play a crucial role in electronic transport properties. We show that the thermoelectric performance of materials is governed by the geometric structure of Bloch wave functions within the…
Can we change the shape of a domain without altering its sizes? By introducing a size-invariant shape transformation, we propose the existence and explore the consequences of a new type of physical effect appearing at the quantum scales,…
The spatial localization of quantum states plays a central role in condensed-matter phenomena, ranging from many-body localization to topological matter. Building on the dissipation-fluctuation theorem, we propose that the localization…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
The modification of electronic band structures and the subsequent tuning of electrical, optical, and thermal material properties is a central theme in the engineering and fundamental understanding of solid-state systems. In this scenario,…
When a quantum many-particle system exists on a randomly diluted lattice, its intrinsic thermal and quantum fluctuations coexist with geometric fluctuations due to percolation. In this paper, we explore how the interplay of these…