Related papers: Quantum geometry in condensed matter
Nonlinear transport phenomena offer an exciting probe into the band geometry and symmetry properties of a system. While most studies on nonlinear transport have looked at second-order nonreciprocal responses in noncentrosymmetric systems,…
Recently, it is shown that, the quantum effects of matter are well described by the conformal degree of freedom of the space-time metric. On the other hand, it is a wellknown fact that according to Einstein's gravity theory, gravity and…
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 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…
The concept of quantum geometry for single-particle states has revolutionized our interpretation of several emergent properties in condensed matter. However, a description of the quantum geometry for interacting particles and an…
Quantized transport not only exist in gapped topological states but also in metallic states. Recently, Kane proposed a quantized nonlinear conductance in ballistic metals whose value is determined by the Euler characteristic of the Fermi…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
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…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
Quantum shape effect appears under the size-invariant shape transformations of strongly confined structures. Such a transformation distinctively influences the thermodynamic properties of confined particles. Due to their characteristic…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
Quantum geometry quantifies how the single-particle Bloch wavefunction changes in phase and amplitude across the Brillouin Zone. In multi-orbital systems where bands have strongly mixed orbital composition, quantum geometry plays a vital…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
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…
Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable…
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…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall…
We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum…