Prethermalization and the Local Robustness of Gapped Systems

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• Prethermalization describes the slow relaxation of quantum systems towards equilibrium.
• Previous studies rigorously analyzed prethermalization in specific frustration-free models.
• Understanding prethermalization is crucial for quantum simulations and topological phases.

Purpose of the Study:

• To prove that prethermalization is a generic property of gapped local many-body quantum systems.
• To establish rigorous bounds on the timescale of prethermalization under small perturbations.
• To extend the understanding of prethermalization beyond frustration-free models.

Main Methods:

• Analysis of quantum dynamics governed by a gapped Hamiltonian (H₀) and a small perturbation (V).
• Focus on the low-energy subspace approximation of the unperturbed Hamiltonian.
• Calculation of correlation functions for local operators to assess approximation accuracy.

Main Results:

• Prethermalization is proven to be a generic property for gapped local quantum systems in any dimension.
• The approximation of dynamics within the low-energy subspace is accurate for stretched exponential timescales (τ∼exp[(Δ/ε)ᵃ], a<1/(2d-1)).
• The result holds regardless of whether the perturbation closes the spectral gap.

Conclusions:

• The findings confirm the robustness of quantum simulations in low-energy subspaces.
• Athermal 'scarred' correlation functions are predicted in gapped systems under generic perturbations.
• The study highlights the long lifetime of false vacua and the robustness of quantum information in various gapped phases.