Related papers: Quantum geometry of common semiconductors
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:…
The calculation of quantum-geometric properties of Bloch electrons -- Berry curvature, quantum metric, orbital magnetic moment and effective mass -- was implemented in a pseudopotential plane-wave code. The starting point was the first…
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…
The rotating shallow water equations (RSWE) are a mainstay of atmospheric and oceanic modeling, and their wave dynamics has close analogues in settings ranging from two-dimensional electron gases to active-matter fluids. While recent work…
The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…
By applying the projector to the filled lattice eigenstates on a specific position, or applying the local electron annihilation operator on the many-body ground state, one can construct a quantum state localized around a specific position…
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…
Quantum metric, a fundamental component of quantum geometry, has attracted broad interest in recent years due to its critical role in various quantum phenomena. Meanwhile, band topology, which serves as an important framework in condensed…
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…
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…
Quantum geometry strongly impacts physical properties in flat-band systems. We consider its role in bosonic condensation and superfluidity on flat bands, and show that the superfluid weight has an important contribution proportional to the…
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 complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…
The quantum metric, a key component of quantum geometry, plays a central role in a wide range of physical phenomena and has been extensively studied in periodic crystals and moir\'{e} materials. Here, we systematically investigate quantum…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
Bosonic Bogoliubov de Gennes (BBdG) Hamiltonians describe the excitations of weakly interacting Bose condensates as well as photonic systems under parametric driving. Their topological features have been studied mainly by utilizing a…