Related papers: Quantum Geometry in Quantum Materials
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner…
The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well-established over four decades of research. More complex aspects of geometry…
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…
This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
We study the relation between the quantum geometry of wave functions and the Landau level (LL) spectrum of two-band Hamiltonians with a quadratic band crossing point (QBCP) in two-dimensions. By investigating the influence of interband…
Chern number is usually characterized by Berry curvature. Here, by investigating the Dirac model of even-dimensional Chern insulator, we give the general relation between Berry curvature and quantum metric, which indicates that the Chern…
Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a…
The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold…
There has been much work in the recent past in developing the idea of quantum geometry to characterize and understand the structure of many-particle states. For mean-field states, the quantum geometry has been defined and analysed in terms…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
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…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…
Bargmann invariants, a class of gauge-invariant quantities arising from the overlaps of quantum state vectors, provide a profound and unifying framework for understanding the geometric structure of quantum mechanics. This survey offers a…
The quantum geometric tensor (QGT), whose real and imaginary parts define the quantum metric and Berry curvature, encodes the intrinsic geometry of quantum states. While electronic QGT has been directly observed and linked to various…
The geometric response of quantum Hall liquids is an important aspect to understand their topological characteristics in addition to the electromagnetic response. According to the Wen-Zee theory, the topological spin is coupled to the…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…