title: Improving the efficiency of hierarchical equations of motion approach and application to coherent dynamics in Aharonov-Bohm interferometers.
abstract: Several recent advancements for the hierarchical equations of motion (HEOM) approach are reported. First, we propose an a priori estimate for the optimal number of basis functions for the reservoir memory decomposition. Second, we make use of the sparsity of auxiliary density operators (ADOs) and propose two ansatzs to screen out all the intrinsic zero ADO elements. Third, we propose a new truncation scheme by utilizing the time derivatives of higher-tier ADOs. These novel techniques greatly reduce the memory cost of the HEOM approach, and thus enhance its efficiency and applicability. The improved HEOM approach is applied to simulate the coherent dynamics of Aharonov-Bohm double quantum dot interferometers. Quantitatively accurate dynamics is obtained for both noninteracting and interacting quantum dots. The crucial role of the quantum phase for the magnitude of quantum coherence and quantum entanglement is revealed.
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Dong
authors.initials: D
authors.lastname: Hou
authors.affiliation: Department of Physics, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, China.
authors.forename: Shikuan
authors.initials: S
authors.lastname: Wang
authors.affiliation: Beijing Computational Science Research Center, Beijing 100084, China.
authors.forename: Rulin
authors.initials: R
authors.lastname: Wang
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: LvZhou
authors.initials: L
authors.lastname: Ye
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: RuiXue
authors.initials: R
authors.lastname: Xu
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Xiao
authors.initials: X
authors.lastname: Zheng
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: YiJing
authors.initials: Y
authors.lastname: Yan