What is the relationship between the quantum metric and the classical metric?
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The quantum metric and the classical metric are distinct from each other . The quantum metric measures the distance between two infinitesimally different quantum states, while the classical metric measures the distance between two infinitesimally different points in phase space . In the context of band theory, the quantum metric has been shown to be proportional to the interband part of the dc electrical conductivity . In the case of semimetals at charge neutrality and systems with highly quenched bandwidth, interband effects due to the quantum metric can be significantly enhanced and even dominate the conductivity . Additionally, for topological flat-band materials of nonzero Chern number, there exists an upper bound for the resistivity due to the common geometrical origin of the quantum metric and Berry curvature .
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15 Nov 2022 | The provided paper does not discuss the relationship between the quantum metric and the classical metric. |
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Open access•Posted Content | The paper shows that the quantum metric introduced on the algebra of continuous functions on the Cantor space is distinct from the classical metric. |
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