Localization and Melting of Interfaces in the Two-Dimensional Quantum Ising Model

Area of Science:

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

Background:

• The two-dimensional quantum Ising model describes systems with competing magnetic orders.
• Understanding nonequilibrium dynamics is key to phenomena like quantum nucleation and false-vacuum decay.
• Rydberg-atom arrays offer a platform for simulating quantum models.

Purpose of the Study:

• To investigate the nonequilibrium evolution of coexisting ferromagnetic domains.
• To analyze the behavior of quantum-fluctuating interfaces in the 2D quantum Ising model.
• To explore the impact of symmetry-breaking fields on system dynamics.

Main Methods:

• Utilizing a holographic mapping to reduce the 2D interface problem to an effective 1D system.
• Identifying emergent interface excitations as an integrable chain of fermionic particles.
• Analyzing integrability breaking mechanisms and calculating timescales for domain melting.

Main Results:

• The quantum interface dynamics map to an integrable fermionic system.
• Integrability is broken by bubble geometry and coupling corrections.
• A lower bound for domain melting timescale is established.
• A symmetry-breaking longitudinal field induces robust 2D ergodicity breaking via Stark many-body localization.

Conclusions:

• The study provides a novel perspective on quantum domain wall dynamics.
• Ergodicity breaking in 2D systems is demonstrated and linked to many-body localization.
• The findings have implications for quantum simulations and understanding complex quantum phenomena.