Eigenstate thermalization in the two-dimensional transverse field Ising model. II. Off-diagonal matrix elements of...

Area of Science:

• Quantum physics
• Condensed matter physics
• Many-body systems

Background:

• The transverse field Ising model is a fundamental model in condensed matter physics.
• Understanding quantum chaos is crucial for characterizing complex quantum systems.
• Matrix elements of observables reveal insights into system dynamics and properties.

Purpose of the Study:

• To analyze the matrix elements of few-body observables in the eigenstates of the 2D transverse field Ising model.
• To connect the onset of quantum chaos with the structure of these matrix elements.
• To test the predictions of random matrix theory and the eigenstate thermalization hypothesis.

Main Methods:

• Symmetry resolution of the two-dimensional transverse field Ising model.
• Analysis of off-diagonal matrix elements of few-body observables.
• Investigation of matrix element behavior as a function of eigenstate energy differences.

Main Results:

• A ratio of variances (diagonal to off-diagonal) of 2 for Hermitian operators is observed in the quantum chaotic regime.
• This ratio aligns with a general result from random matrix theory.
• The behavior of off-diagonal matrix elements supports the eigenstate thermalization hypothesis ansatz.

Conclusions:

• The study provides a link between quantum chaos and the statistical properties of matrix elements.
• The findings validate predictions from random matrix theory in a specific quantum chaotic system.
• The results contribute to the understanding of thermalization in many-body quantum systems.