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arXiv:quant-ph/0701061

The differential information-geometry of quantum phase transitions

Paolo Zanardi A, Paolo Giorda, Marco Cozzini

Published Jan 11, 2007• 2 citations
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Abstract

The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with the quantum phase transitions featured by the corresponding system. This approach provides a universal conceptual framework to study quantum critical phenomena which is differential-geometric and information-theoretic at the same time.

DOI
10.48550/arxiv.quant-ph/0701061

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The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with the quantum phase transitions featured by the corresponding system. This approach provides a universal conceptual framework to study quantum critical phenomena which is differential-geometric and information-theoretic at the same time.
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