Avalanche of entanglement and correlations at quantum phase transitions

  • Konstantin V. Krutitsky, Andreas Osterloh, Ralf Schützhold
  • Scientific Reports, June 2017, Nature
  • DOI: 10.1038/s41598-017-03402-8

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.

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.


Dr. Andreas Osterloh

There is no way to come across a quantum phase transition, not with aproximations from a mean-field point, nor with adiabatic means, since the gap closes at the critical point and the time required to get an adiabatic situation would blow up. There is given also strong evidence in the literature that this is true for whatever problems to solve adiabatically and which are NP-hard (maybe the unsolved problem in complexity theory, namely to show that NP>P, is also related to it). Concerning the multi-partite entanglement for the Ising-type models, it is to my knowledge the first attempt at all to overcome the convex-roof construction in entanglement theory in a model relevant for condensed matter.

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The following have contributed to this page: Dr. Andreas Osterloh

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