Subsystem eigenstate thermalization hypothesis

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Condensed matter physics

Background:

• The eigenstate thermalization hypothesis (ETH) explains how isolated quantum systems reach thermal equilibrium.
• Canonical typicality provides a qualitative understanding of thermalization in chaotic quantum systems.

Purpose of the Study:

• To propose a refined formulation of the ETH, termed subsystem ETH, applicable to chaotic quantum systems.
• To define the conditions under which thermalization occurs for observables within a subsystem.
• To investigate the behavior of entanglement entropies for subsystems of varying sizes.

Main Methods:

• Formulating subsystem ETH using reduced density matrices of quantum subsystems.
• Analyzing the limits of small and comparable subsystem sizes relative to their complements.
• Calculating volume-proportional contributions to von Neumann and Rényi entanglement entropies.
• Conducting numerical simulations on a one-dimensional Ising spin chain.

Main Results:

• Subsystem ETH precisely defines the observables within a subsystem that exhibit eigenstate thermalization.
• The study outlines methods for calculating entanglement entropies in specific subsystem size regimes.
• Numerical evidence supporting the subsystem ETH formulation was obtained from the Ising spin chain model.

Conclusions:

• Subsystem ETH offers a strong formulation of thermalization for subsystems in chaotic quantum systems.
• The proposed framework provides insights into the relationship between quantum information and thermalization.
• The findings are validated by numerical simulations, confirming the utility of subsystem ETH.