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Quantum geometry of non-Hermitian systems
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The Berry curvature characterizes one aspect of the geometry of quantum states. It materializes, among other consequences, as an anomalous velocity of wave packets. In non-Hermitian systems, wave packet dynamics is enriched by additional terms that can be expressed as generalizations of the Berry connection to non-orthogonal eigenstates. Here, we contextualize these anomalous non-Hermitian contributions by showing that they directly arise from the geometry of the underlying quantum states as corrections to the distance between left and perturbed right eigenstates. By calculating the electric susceptibility for a single-band wave packet and comparing it with the wave packet's localization, we demonstrate that these terms can, in some circumstances, lead to a violation of fluctuation-dissipation relations in non-Hermitian systems. We discuss experimental signatures in terms of response functions and transport signatures.
Forward citations
Cited by 3 Pith papers
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Quantum geometry of the non-Hermitian skin effect
The localization length of the non-Hermitian skin effect is encoded in the quantum metric of right eigenstates, exhibiting power-law divergences at gapless points and discontinuities at cusps of the generalized Brillo...
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Topological Order and Non-Hermitian Skin Effect in Generalized Ideal Chern Bands
A non-Hermitian Kapit-Mueller model hosts an exactly flat, purely real ideal Chern band whose interacting states are skin-Laughlin states on a cylinder and destabilize on a torus above a critical non-Hermiticity.
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Non-Bloch Quantum Geometry of Non-Hermitian Systems
Establishes exact equivalence between real-space and non-Bloch integrated quantum metrics for non-Hermitian open-boundary systems and shows the latter gives the gauge-invariant spread of non-Bloch Wannier functions.
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