Avalanche of entanglement and correlations at quantum phase transitions

What is it about?

It is about correlation functions and their behavior at quantum phase transitions. It demonstrates that coming from a mean field solution the hierarchy of the correlation functions with orders of the interaction parameter is inverted when coming close to the critical point. This is shown to apply for two models: the integrable one dimensional Ising-type spin chain in a transverse external field, and the Bose-Hubbard model. Therefore every approximation method where this hierarchy enters will fail. The other central result is that reduced density matrices of few particles will have approximately two non-zero eigenvalues only for the models of the Ising type; hence can we apply approximation schemes to their entanglement giving results for up to four sites for the first time. The results are a strong evidence for an "avalanche of entanglement" happening when crossing the critical point.

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Why is it important?

Coming from a mean field solution, whatever approximation we are applying to the system, somehow contains the hierarchy of correlations and will fail well before reaching the critical point. The convex-roof construction is something that obstaculates the calculation of many-particle entanglement; this is the first time it can be overcome and gives results for three and four sites.

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