Spins Dynamics in a Dissipative Environment: Hierarchal Equations of Motion Approach Using a Graphics Processing Unit...

Area of Science:

• Quantum physics
• Condensed matter physics
• Computational physics

Background:

• Understanding quantum non-Markovian dynamics is crucial for complex systems.
• Simulating large quantum systems requires efficient numerical methods.
• Quantum spin glasses exhibit complex behaviors influenced by temperature and interactions.

Purpose of the Study:

• To develop a rigorous and nonperturbative numerical method for quantum non-Markovian system-bath dynamics.
• To investigate the spin relaxation dynamics in quantum spin glass systems using the developed code.
• To analyze the temperature dependence of spin relaxation pathways.

Main Methods:

• Developed a graphics processor unit (GPU)-accelerated code for reduced hierarchy equations of motion (HEOM).
• Employed Padé spectrum decomposition (PSD) for HEOM construction and exponential integrators.
• Calculated the free induction decay signal for quantum spin glass models on triangular lattices.

Main Results:

• The GPU-accelerated HEOM code can handle systems with up to 4096 energy states.
• Spins in the quantum spin glass model relax faster at lower temperatures due to quantum coherent states.
• This contrasts with classical systems where spin relaxation slows down at lower temperatures due to suppressed thermal activation.
• Spin decay patterns showed qualitative similarity across different lattice sizes.

Conclusions:

• The developed computational tool enables rigorous study of large quantum systems.
• Quantum coherence plays a significant role in spin relaxation dynamics at low temperatures.
• The findings provide insights into the non-classical behavior of quantum spin glasses.