Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions

Area of Science:

• Quantum physics
• Many-body systems
• Condensed matter physics

Background:

• Long-range interacting systems like nitrogen vacancy centers and trapped ions are used to study nonequilibrium many-body phenomena.
• Driving these systems can realize effective Hamiltonians with unique physics compared to short-range systems.

Purpose of the Study:

• Derive rigorous bounds on linear response energy absorption rates for periodically driven, long-range interacting spin or fermion systems.
• Investigate the high-temperature behavior of disorder-averaged energy absorption rates.
• Provide evidence for prethermal plateaus governed by effective static Hamiltonians.

Main Methods:

• Derivation of general rigorous bounds on energy absorption rates.
• Analysis of systems with sign-changing, power-law decaying (1/r^α, α>d/2) long-range interactions.
• Numerical simulations to support theoretical findings.

Main Results:

• Energy absorption rate decays exponentially with driving frequency at high temperatures.
• Strong evidence for a prethermal plateau where dynamics are governed by an effective static Hamiltonian for extended periods.
• Rigorous bounds established for linear response energy absorption.

Conclusions:

• The findings are crucial for understanding heating timescales in long-range interacting systems.
• New dynamical regimes governed by effective Hamiltonians can be explored in these systems.
• The study highlights the importance of long-range interactions in driving novel quantum phenomena.