Absence of thermalization in nonintegrable systems

Area of Science:

• Quantum physics
• Statistical mechanics
• Condensed matter theory

Background:

• Understanding thermalization in closed quantum systems is a fundamental challenge.
• The role of integrability and entanglement in equilibration remains an active area of research.
• Previous studies often focused on integrable models or specific types of dynamics.

Purpose of the Study:

• To establish a link between unitary relaxation dynamics and entanglement in the energy eigenbasis.
• To investigate memory effects in non-integrable systems after a quantum quench.
• To clarify the applicability of maximum entropy ensembles in describing equilibrium states.

Main Methods:

• Analysis of unitary relaxation dynamics in closed many-body systems.
• Calculation of entanglement properties in the energy eigenbasis.
• Comparison of equilibrium state descriptions across different models.

Main Results:

• A direct link between relaxation dynamics and energy eigenbasis entanglement was established.
• Memory of initial conditions persists in reduced states even in non-integrable systems.
• Maximum entropy ensembles (e.g., generalized Gibbs ensemble) describe equilibrium states irrespective of integrability.

Conclusions:

• Equilibration in closed quantum systems does not necessarily erase all information about initial conditions.
• The framework applies to both integrable and non-integrable models, unifying descriptions of thermalization.
• The study contributes to ongoing debates on thermalization, integrability, and the role of localization.