Related papers: Percolation from Quantum Metric in Flat-Band Deloc…
Quantum site percolation as a limiting case of binary alloy is studied numerically in 2D within the tight-binding model. We address the transport properties in all regimes - ballistic, diffusive (metallic), localized and crossover between…
The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and…
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is…
Percolation, describing critical behaviors of phase transition in a geometrical context, prompts wide investigations in natural and social networks as a fundamental model. The introduction of quantum-intrinsic interference and tunneling…
The presence of localized boundary modes is an unambiguous hallmark of topological quantum matter. While these modes are typically protected by topological invariants such as the Chern number, here we demonstrate that the {\it quantum…
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:…
Over the years, Berry curvature, which is associated with the imaginary part of the quantum geometric tensor, has profoundly impacted many branches of physics. Recently, quantum metric, the real part of the quantum geometric tensor, has…
We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with…
Entanglement measures have emerged as one of the versatile probes to diagnose quantum phases and their transitions. Universal features in them expand their applicability to a range of systems, including those with quenched disorder. In this…
The interplay of geometric randomness and strong quantum fluctuations is an exciting topic in quantum many-body physics, leading to the emergence of novel quantum phases in strongly correlated electron systems. Recent investigations have…
We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using 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…
Most of the investigations to date on tight-binding, quantum percolation models focused on the quantum percolation threshold, i.e., the analogue to the Anderson transition. It appears to occur if roughly 30% of the hopping terms are…
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…
The quantum metric is a central quantity of band theory but has so far not been related to many response coefficients due to its nonclassical origin. However, within a newly developed Kubo formalism for fast relaxation, the decomposition of…
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…
Our previous understanding of electronic transport in disordered systems was based on the assumption that there is a finite Fermi velocity for the relevant electrons. The Fermi velocity determines important length scales in disordered…
The Localization Landscape Theory (LLT) provides a classical picture of Anderson localization by introducing an effective confining potential whose percolation is proposed to coincide with the mobility edge. Although this proposal shows…