title: Spins Dynamics in a Dissipative Environment: Hierarchal Equations of Motion Approach Using a Graphics Processing Unit (GPU).
abstract: A system with many energy states coupled to a harmonic oscillator bath is considered. To study quantum non-Markovian system-bath dynamics numerically rigorously and nonperturbatively, we developed a computer code for the reduced hierarchy equations of motion (HEOM) for a graphics processor unit (GPU) that can treat the system as large as 4096 energy states. The code employs a Padé spectrum decomposition (PSD) for a construction of HEOM and the exponential integrators. Dynamics of a quantum spin glass system are studied by calculating the free induction decay signal for the cases of 3 × 2 to 3 × 4 triangular lattices with antiferromagnetic interactions. We found that spins relax faster at lower temperature due to transitions through a quantum coherent state, as represented by the off-diagonal elements of the reduced density matrix, while it has been known that the spins relax slower due to suppression of thermal activation in a classical case. The decay of the spins are qualitatively similar regardless of the lattice sizes. The pathway of spin relaxation is analyzed under a sudden temperature drop condition. The Compute Unified Device Architecture (CUDA) based source code used in the present calculations is provided as Supporting Information .
authors.affiliation: Department of Chemistry, Graduate School of Science, Kyoto University , Sakyoku, Kyoto 606-8502, Japan.
authors.forename: Masashi
authors.initials: M
authors.lastname: Tsuchimoto
authors.affiliation: Department of Chemistry, Graduate School of Science, Kyoto University , Sakyoku, Kyoto 606-8502, Japan.
authors.forename: Yoshitaka
authors.initials: Y
authors.lastname: Tanimura
mesh_terms: D000465:Algorithms; D011789:Quantum Theory; D013696:Temperature