Nonthermal States Arising from Confinement in One and Two Dimensions

Area of Science:

• Quantum physics
• Condensed matter theory
• Statistical mechanics

Background:

• The quantum Ising model is a fundamental model in condensed matter physics.
• Understanding the nature of eigenstates and thermalization is crucial for quantum systems.

Purpose of the Study:

• To investigate the impact of confinement on eigenstates in the quantum Ising model.
• To analyze the resulting excitation spectrum and dynamical behavior.

Main Methods:

• Analysis of both continuum and lattice quantum Ising models in 1D and 2D.
• Examination of the excitation spectrum under a confining longitudinal field.
• Investigation of postquench dynamics, including entanglement entropy growth.

Main Results:

• Confinement induces nonthermal eigenstates in the ordered phase of the quantum Ising model.
• A confining field replaces the two-particle continuum with discrete "meson" modes (confined domain wall pairs).
• These meson states show a lack of hybridization and persist above the two-meson threshold, leading to suppressed thermalization and anomalous dynamics.

Conclusions:

• Nonthermal eigenstates are a robust feature of confined quantum Ising models in the ordered phase.
• The observed lack of thermalization in these states challenges standard statistical mechanics predictions.
• These findings have implications for understanding quantum dynamics and the emergence of thermalization.