Superdiffusion, normal diffusion, and chaos in semiclassical Bose-Hubbard chains

Area of Science:

• Quantum many-body physics
• Statistical mechanics
• Condensed matter theory

Background:

• The Bose-Hubbard model describes interacting bosons in a lattice.
• Understanding correlation function dynamics is crucial for characterizing quantum systems.
• Semiclassical approximations offer insights into complex quantum behavior.

Purpose of the Study:

• To investigate the evolution of two-point correlation functions in the 1D Bose-Hubbard model.
• To analyze the role of superdiffusion and its dependence on initial conditions and system parameters.
• To explore the transition from superdiffusion to normal diffusion and its relation to nonintegrability and chaos.

Main Methods:

• Utilizing the truncated Wigner approximation (TWA).
• Incorporating quantum jumps as first-order corrections to TWA.
• Analyzing the semiclassical regime of the Bose-Hubbard model.

Main Results:

• Observed strong superdiffusion at early times with universal integer exponents.
• Demonstrated that superdiffusion is insensitive to system parameters and chaos.
• Identified a crossover to normal diffusion at later times, robust under strong nonintegrability.
• Found that strong nonintegrability leads to a homogeneous state, while weak nonintegrability preserves oscillations.

Conclusions:

• The observed superdiffusion is an early-time phenomenon, not related to prethermalization or thermalization.
• Superdiffusion is linked to a specific scaling symmetry of the Bose-Hubbard Hamiltonian.
• System behavior at later times depends on the degree of nonintegrability, with chaos playing a significant role.