Two-point versus multipartite entanglement in quantum phase transitions.

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.

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.