Related papers: Quantum Information Metric and Berry Curvature fro…
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…
We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The…
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…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
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…
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 geometry of the parameter space is encoded by the quantum geometric tensor, which captures fundamental information about quantum states and contains both the quantum metric tensor and the curvature of the Berry connection. We present a…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
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…
We present a reformulation of quantum adiabatic theory in terms of an emergent electromagnetic framework, emphasizing the physical consequences of geometric structures in parameter space. Contrary to conventional approaches, we demonstrate…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of…
In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this…
The eigenvalues of a parameter-dependent Hamiltonian matrix form a band structure in parameter space. In such $N$-band systems, the quantum geometric tensor (QGT), consisting of the Berry curvature and quantum metric tensors, is usually…
We present a geometric characterization of the ferrotoroidic moment in terms of a set of Abelian Berry phases. We also introduce a fundamental complex quantity which provides an alternative way to calculate the ferrotoroidic moment and its…
We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
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…
The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that…