Many-body collective fluctuations generate a dynamical Berry curvature that is invisible to optics but isolable in antisymmetric RIXS channels of P-T-symmetric systems.
Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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 complex tensor with the real part serving as the Riemannian metric that measures the `quantum distance', and the imaginary part being the Berry curvature. Following a physical introduction of the basic formalism, we illustrate its physical significance in both the adiabatic and non-adiabatic systems.
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Post-quench dynamics of the quantum geometric tensor in 1D periodic systems are governed by initial-state geometric quantities and post-quench band properties such as Berry connection and group velocities, providing a probe for nonequilibrium phenomena.
Gauge invariance of the quantum geometric tensor implies zero modes of a non-abelian Dirac operator in band insulators whose theta-function solutions define CP^{N-1} spaces and generalize vortexability criteria with links to lowest Landau level algebra.
The paper proposes the MAPS framework with n projectional intersecting spatial axes for visualizing qudit state-spaces and introduces novel d-valued phase axial-based gates.
The Bures metric near rank-changing points is a coordinate artifact for N=2 but reduces to a conical metric with genuine curvature singularities for N>=3, illustrated by specific Lindblad processes.
This thesis explores geometric and dynamical properties of entanglement in two- and many-body spin systems under XXZ and Ising interactions using phase space and Fubini-Study geometry.
citing papers explorer
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Geometric curvature driven by many-body collective fluctuations
Many-body collective fluctuations generate a dynamical Berry curvature that is invisible to optics but isolable in antisymmetric RIXS channels of P-T-symmetric systems.
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Evolution of quantum geometric tensor of 1D periodic systems after a quench
Post-quench dynamics of the quantum geometric tensor in 1D periodic systems are governed by initial-state geometric quantities and post-quench band properties such as Berry connection and group velocities, providing a probe for nonequilibrium phenomena.
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Zero modes of non-abelian Dirac operator in topologically non-trivial band insulator
Gauge invariance of the quantum geometric tensor implies zero modes of a non-abelian Dirac operator in band insulators whose theta-function solutions define CP^{N-1} spaces and generalize vortexability criteria with links to lowest Landau level algebra.
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MAPS: A Novel Multi-Axial Projective Sphere for Geometrically Visualizing Higher d-Valued Quantum State-Space of Qudits
The paper proposes the MAPS framework with n projectional intersecting spatial axes for visualizing qudit state-spaces and introduces novel d-valued phase axial-based gates.
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Geometry near rank-changing points on the mixed-state manifold: Bures metric, conical singularities, and Lindblad dynamics
The Bures metric near rank-changing points is a coordinate artifact for N=2 but reduces to a conical metric with genuine curvature singularities for N>=3, illustrated by specific Lindblad processes.
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Exploring the Geometric and Dynamical Properties of Spin Systems and Their Interplay with Quantum Entanglement
This thesis explores geometric and dynamical properties of entanglement in two- and many-body spin systems under XXZ and Ising interactions using phase space and Fubini-Study geometry.