Related papers: Geometric contribution to the Goldstone mode in sp…
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…
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:…
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
Quantum geometry, including quantum metric and Berry curvature, which describes the topology of electronic states, can induce fascinating physical properties. Symmetry-dependent nonlinear transport has emerged as a sensitive probe of these…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
A critical result in superconductivity is that flat bands, though dispersionless, can still host nonzero superfluid weight due to quantum geometry. We show that the derivation of the mean field superfluid weight in previous literature is…
The space of quantum states can be endowed with a metric structure using the second order derivatives of the relative entropy, giving rise to the so-called Kubo-Mori-Bogoliubov inner product. We explore its geometric properties on the…
Making use of coherence and entanglement as metrological quantum resources allows to improve the measurement precision from the shot-noise- or quantum limit to the Heisenberg limit. Quantum metrology then relies on the availability of…
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…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
We investigate the impacts of the quantum geometry of Bloch states, specifically through the band-resolved quantum-metric tensor, on Cooper pairing and flat-band superconductivity in a three-dimensional pyrochlore-Hubbard model. First we…
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…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
The superfluid weight of an isolated flat band in multi-orbital superconductors contains contributions from the band's quantum metric and a lattice geometric term that depends on the orbital positions in the lattice. Since the superfluid…
The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the…
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…
Coulomb repulsion can, counterintuitively, mediate Cooper pairing via the Kohn-Luttinger mechanism. However, it is commonly believed that observability of the effect requires special circumstances -- e.g., vicinity of the Fermi level to van…
We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric…
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…