Ring frustration and factorizable correlation functions of critical spin rings

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory

Background:

• Nonlocality is a key feature in quantum many-body systems.
• Understanding nonlocality in the thermodynamic limit is crucial for characterizing complex quantum phases.

Purpose of the Study:

• To establish and quantify nonlocality in a many-body system within the thermodynamic limit.
• To investigate the impact of lattice structure (odd vs. even sites) on nonlocality.
• To explore the application of finite-size scaling analysis to nonlocality measures.

Main Methods:

• Exact solution of the critical transverse Ising ring model.
• Calculation of nonlocal factors from the factorizable correlation function.
• Numerical analysis of nonlocal factors for isotropic XY and spin-1/2 Heisenberg models.

Main Results:

• The study establishes a method to define and calculate nonlocality in the thermodynamic limit.
• A clear distinction in nonlocality is observed between periodic chains with odd and even numbers of lattice sites.
• Finite-size scaling analysis is successfully applied to quantify nonlocality in other models.

Conclusions:

• Nonlocality can be rigorously defined and analyzed in the thermodynamic limit using exactly solvable models.
• The parity of lattice sites significantly influences nonlocality, even for large systems.
• The developed framework is applicable to other quantum models, aiding in the study of their nonlocality.