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Related Experiment Videos

Two-point versus multipartite entanglement in quantum phase transitions.

Alberto Anfossi1, Paolo Giorda, Arianna Montorsi

  • 1Dipartimento di Fisica del Politecnico, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.

Physical Review Letters
|August 11, 2005
PubMed
Summary

We analyze quantum correlations in a solvable model, identifying quantum phase transitions (QPTs) using entanglement singularities. This method distinguishes between two-point and shared correlations driving QPTs in quantum systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory

Background:

  • The extended Hubbard model in one dimension exhibits complex quantum phase transitions (QPTs).
  • Understanding the nature of correlations driving these QPTs is crucial for characterizing quantum systems.

Purpose of the Study:

  • To analyze correlations between subsystems in an exactly solvable extended Hubbard model.
  • To identify the types of quantum correlations (two-point or shared) responsible for QPTs.
  • To establish a method for recognizing these correlations using entanglement measures.

Main Methods:

  • Exact solution of the one-dimensional extended Hubbard model.
  • Analysis of singularities in single-site entanglement to reproduce the T=0 phase diagram.
  • Comparison of single-site entanglement and quantum mutual information.

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Main Results:

  • The T=0 phase diagram is accurately reproduced by studying single-site entanglement singularities.
  • A method is presented to distinguish between two-point and shared quantum correlations driving QPTs.
  • The approach is general and applicable to systems with any number of degrees of freedom per site (D).
  • The role of negativity as a measure of bipartite entanglement at transitions is discussed.

Conclusions:

  • Singularities in single-site entanglement provide an exact method to map quantum phase diagrams.
  • Comparing entanglement measures reveals the nature of correlations underlying quantum phase transitions.
  • This work offers a benchmark for entanglement measures and advances the understanding of quantum correlations in many-body systems.