Related papers: Quantum geometric tensor and quantum phase transit…
We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and…
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 relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this…
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying…
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 geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…
The manifold of ground states of a family of quantum Hamiltonians can be endowed with a quantum geometric tensor whose singularities signal quantum phase transitions and give a general way to define quantum phases. In this paper, we show…
It is of high interest, in the context of Adiabatic Quantum Computation, to better understand the complex dynamics of a quantum system subject to a time-dependent Hamiltonian, when driven across a quantum phase transition. We present here…
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 propose a generic protocol to experimentally measure the quantum metric tensor, a fundamental geometric property of quantum states. Our method is based on the observation that the excitation rate of a quantum state directly relates to…
Quantum coherence reflects the origin of quantumness and might be capable of extracting the subtle nature of a system. We investigate the ground-state coherence and steered coherence in the Lipkin-Meshkov-Glick model and show that they…
The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous…
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…
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…
Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is at the core of modern physics. The Quantum Geometric Tensor (QGT) is a central physical object in this regard, encoding…
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…
The quantum geometric tensor (QGT) characterizes the complete geometric properties of quantum states, with the symmetric part being the quantum metric, and the antisymmetric part being the Berry curvature. We propose a generic Hamiltonian…
Quantum phase transitions have been shown to be highly beneficial for quantum sensing, owing to diverging quantum Fisher information close to criticality. In this work we consider a periodically modulated Lipkin-Meshkov-Glick model to show…
Lipkin model of arbitrary particle-number N is studied in terms of exact differential-operator representation of spin-operators from which we obtain the low-lying energy spectrum with the instanton method of quantum tunneling. Our new…
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…