Eigenstate entanglement entropy in the integrable spin-1/2 XYZ model

Area of Science:

• Quantum Many-Body Physics
• Condensed Matter Theory
• Statistical Mechanics

Background:

• Entanglement entropy quantifies quantum correlations in many-body systems.
• Integrable models exhibit unique properties distinct from quantum-chaotic systems.
• Highly excited eigenstates in quantum systems are crucial for understanding thermalization and statistical properties.

Purpose of the Study:

• To investigate the average and standard deviation of entanglement entropy in highly excited eigenstates of the integrable spin-1/2 XYZ chain.
• To compare these properties with those of quantum-chaotic interacting models.
• To analyze the impact of U(1) symmetry and supersymmetry on entanglement entropy.

Main Methods:

• Numerical analysis of the spin-1/2 XYZ chain.
• Calculation of entanglement entropy for highly excited eigenstates.
• Comparison of results with theoretical predictions for integrable and quantum-chaotic systems.

Main Results:

• The average entanglement entropy in integrable models shows a smaller volume-law coefficient than in quantum-chaotic models.
• The normalized standard deviation of entanglement entropy decays polynomially with system size in integrable models, contrasting with exponential decay in chaotic models.
• Degeneracies at the supersymmetric point were resolved for average entanglement entropy calculations.

Conclusions:

• Integrability in spin-1/2 chains fundamentally alters the behavior of entanglement entropy in highly excited eigenstates.
• The findings highlight key differences between integrable and quantum-chaotic systems regarding quantum correlations.
• This work provides significant numerical evidence supporting theoretical insights into quantum information in diverse quantum models.