Revealing tensor monopoles through quantum-metric measurements

Abstract

Monopoles are intriguing topological objects, which play a central role in gauge theories and topological states of matter. While conventional monopoles are found in odd-dimensional flat spaces, such as the Dirac monopole in three dimensions and the non-Abelian Yang monopole in five dimensions, more exotic objects were predicted to exist in even dimensions. This is the case of "tensor monopoles", which are associated with generalized (tensor) gauge fields, and which can be defined in four dimensional flat spaces. In this work, we investigate the possibility of creating and measuring such a tensor monopole, by introducing a realistic three-band model defined over a four-dimensional parameter space. Our probing method is based on the observation that the topological charge of this tensor monopole, which we relate to a generalized Berry curvature, can be directly extracted from the quantum metric. We propose a realistic three-level atomic system, where tensor monopoles could be generated and revealed through quantum-metric measurements.

4+4 pages, 2 figures, Revised version containing new appendices

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Cited by in corpus (55)

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• Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena
• Measurement of Topological Order based on Metric-Curvature Correspondence
• Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers
• Tensor Berry connections and their topological invariants
• Ground-state quantum geometry in superconductor-quantum dot chains
• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Wave-function geometry of band crossing points in two-dimensions
• Dual Haldane sphere and quantized band geometry in chiral multifold fermions
• Non-Abelian tensor Berry connections in multi-band topological systems
• Revealing Chern number from quantum metric
• Quantum Fluctuation of the Quantum Geometric Tensor and its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems
• Massless multifold Hopf semimetals
• Computing observables without eigenstates: applications to Bloch Hamiltonians
• Fidelity and Uhlmann connection analysis of topological phase transitions in two dimensions
• Tensor Monopoles in superconducting systems
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Identifying non-Hermitian critical points with quantum metric
• Local geometry and quantum geometric tensor of mixed states
• Quantum geometry of singlet superconductors
• Skin Effect in Quadratic Lindbladian Systems: an Adjoint Fermion Approach
• Tensor monopoles and negative magnetoresistance effect in optical lattices
• Band geometry from position-momentum duality at topological band crossings
• Link between \emph{Zitterbewegung} and topological phase transition
• Revealing divergent length scales using quantum Fisher information in the Kitaev honeycomb model
• Geometry of the parameter space of a quantum system: Classical point of view
• Quantum multiparameter estimation enhanced by a topological phase transition
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Fermion-fermion duality in 3+1 dimensions
• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Second Euler number in four dimensional synthetic matter
• State Space Geometry of the Spin-1 Antiferromagnetic Heisenberg Chain
• The Fermi gerbe of Weyl semimetals
• A synthetic monopole source of Kalb-Ramond field in diamond
• Generalized quantum geometric tensor for excited states using the path integral approach
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Time-dependent quantum geometric tensor and some applications
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• Geometric semimetals and their simulation in synthetic matter
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Quantum geometric tensors from sub-bundle geometry
• An exceptional surface and its topology
• Universal intrinsic higher-rank spin Hall effect
• Topological dynamics of adiabatic cat states
• Evolution of quantum geometric tensor of 1D periodic systems after a quench