Time reparametrization group and the long time behavior in quantum glassy systems

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Mechanics

Background:

• The Sherrington-Kirkpatrick (SK) model is a fundamental model in statistical mechanics for studying spin glasses.
• Understanding the long-time dynamics and aging behavior of disordered systems is crucial.
• Quantum effects in such models can significantly alter their classical behavior.

Purpose of the Study:

• To analyze the long-time dynamics of a quantum version of the Sherrington-Kirkpatrick model.
• To investigate the role of quantum fluctuations in the aging regime.
• To understand the relationship between classical and quantum dynamics in this model.

Main Methods:

• Employing time reparametrizations of dynamical equations, analogous to renormalization group transformations.
• Analyzing the model's behavior near a reparametrization group (R(p)G) fixed point.
• Comparing the dynamics of the quantum model with its classical counterpart.

Main Results:

• The long-time behavior is governed by a fixed point of the classical dynamics within the reparametrization group framework.
• Quantum terms in the dynamical equations are found to be irrelevant in the aging regime.
• This irrelevance explains why the out-of-equilibrium fluctuation-dissipation relation retains its classical nature.

Conclusions:

• The aging dynamics of the quantum SK model are dominated by classical behavior.
• Quantum fluctuations do not alter the fundamental nature of the fluctuation-dissipation relation in the long-time limit.
• The study provides insights into the interplay between quantum mechanics and classical statistical mechanics in complex systems.