Non universality of entanglement convertibility

Abstract

Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that present phase transitions of different orders. For this purpose, we evaluate the local convertibility between bipartite ground states. Our results suggest that the operational properties, related to non-analyticities of the entanglement spectrum, are good detectors of explicit symmetries of the model, but not necessarily of phase transitions. We also show that thermodynamically equivalent phases, such as Luttinger liquids, may display different convertibility properties depending on the underlying microscopic model.

arXiv comment5 pages + references, 4 figures - improved version

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• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• Scaling of the entanglement spectrum in driving critical dynamics
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Entanglement spectra of superconductivity ground states on the honeycomb lattice