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Zhang D, Zuo L, Ye L, Chen ZH, Wang Y, Xu RX, Zheng X, Yan Y. Hierarchical equations of motion approach for accurate characterization of spin excitations in quantum impurity systems. J Chem Phys 2023; 158:014106. [PMID: 36610957 DOI: 10.1063/5.0131739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Recent technological advancement in scanning tunneling microscopes has enabled the measurement of spin-field and spin-spin interactions in single atomic or molecular junctions with an unprecedentedly high resolution. Theoretically, although the fermionic hierarchical equations of motion (HEOM) method has been widely applied to investigate the strongly correlated Kondo states in these junctions, the existence of low-energy spin excitations presents new challenges to numerical simulations. These include the quest for a more accurate and efficient decomposition for the non-Markovian memory of low-temperature environments and a more careful handling of errors caused by the truncation of the hierarchy. In this work, we propose several new algorithms, which significantly enhance the performance of the HEOM method, as exemplified by the calculations on systems involving various types of low-energy spin excitations. Being able to characterize both the Kondo effect and spin excitation accurately, the HEOM method offers a sophisticated and versatile theoretical tool, which is valuable for the understanding and even prediction of the fascinating quantum phenomena explored in cutting-edge experiments.
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Affiliation(s)
- Daochi Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lijun Zuo
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lyuzhou Ye
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zi-Hao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Research Center for Physical Sciences at the Microscale and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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Gong H, Ullah A, Ye L, Zheng X, Yan Y. Quantum entanglement of parallel-coupled double quantum dots: A theoretical study using the hierarchical equations of motion approach. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1806138] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Hong Gong
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Arif Ullah
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - LvZhou Ye
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale & iChEM, University of Science and Technology of China, Hefei 230026, China
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Maslova NS, Arseyev PI, Mantsevich VN. Collective spin correlations and entangled state dynamics in coupled quantum dots. Phys Rev E 2018; 97:022135. [PMID: 29548085 DOI: 10.1103/physreve.97.022135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Indexed: 06/08/2023]
Abstract
Here we demonstrate that the dynamics of few-electron states in a correlated quantum-dot system coupled to an electronic reservoir is governed by the symmetry properties of the total system leading to the collective behavior of all the electrons. Time evolution of two-electron states in a correlated double quantum dot after coupling to the reservoir has been analyzed by means of kinetic equations for pseudoparticle occupation numbers with constraint on possible physical states. It was revealed that the absolute value of the spin correlation function and the degree of entanglement for two-electron states could considerably increase after coupling to the reservoir. The obtained results demonstrate the possibility of a controllable tuning of both the spin correlation function and the concurrence value in a coupled quantum-dot system by changing of the gate voltage applied to the barrier separating the dots.
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Affiliation(s)
- N S Maslova
- Department of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - P I Arseyev
- P.N. Lebedev Physical Institute RAS, 119991 Moscow, Russia
| | - V N Mantsevich
- Department of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
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Dong B, Ding GH, Lei XL. Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:205303. [PMID: 25950191 DOI: 10.1088/0953-8984/27/20/205303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.
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Affiliation(s)
- B Dong
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200240, People's Republic of China
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Hou D, Wang S, Wang R, Ye L, Xu R, Zheng X, Yan Y. Improving the efficiency of hierarchical equations of motion approach and application to coherent dynamics in Aharonov–Bohm interferometers. J Chem Phys 2015; 142:104112. [DOI: 10.1063/1.4914514] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Fratini F, Mascarenhas E, Safari L, Poizat JP, Valente D, Auffèves A, Gerace D, Santos MF. Fabry-Perot interferometer with quantum mirrors: nonlinear light transport and rectification. PHYSICAL REVIEW LETTERS 2014; 113:243601. [PMID: 25541772 DOI: 10.1103/physrevlett.113.243601] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2014] [Indexed: 06/04/2023]
Abstract
Optical transport represents a natural route towards fast communications, and it is currently used in large scale data transfer. The progressive miniaturization of devices for information processing calls for the microscopic tailoring of light transport and confinement at length scales appropriate for upcoming technologies. With this goal in mind, we present a theoretical analysis of a one-dimensional Fabry-Perot interferometer built with two highly saturable nonlinear mirrors: a pair of two-level systems. Our approach captures nonlinear and nonreciprocal effects of light transport that were not reported previously. Remarkably, we show that such an elementary device can operate as a microscopic integrated optical rectifier.
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Affiliation(s)
- F Fratini
- Departamento de Física, Universidade Federal de Minas Gerais, CP 702, 30123-970 Belo Horizonte, Brazil and Université Grenoble Alpes, Institut NÉEL, F-38042 Grenoble, France and CNRS, Institut NÉEL, F-38042 Grenoble, France and Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu, Finland
| | - E Mascarenhas
- Departamento de Física, Universidade Federal de Minas Gerais, CP 702, 30123-970 Belo Horizonte, Brazil
| | - L Safari
- Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu, Finland and IST Austria, Am Campus 1, A-3400 Klosterneuburg, Austria
| | - J-Ph Poizat
- Université Grenoble Alpes, Institut NÉEL, F-38042 Grenoble, France and CNRS, Institut NÉEL, F-38042 Grenoble, France
| | - D Valente
- Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá MT, Brazil
| | - A Auffèves
- Université Grenoble Alpes, Institut NÉEL, F-38042 Grenoble, France and CNRS, Institut NÉEL, F-38042 Grenoble, France
| | - D Gerace
- Dipartimento di Fisica, Università di Pavia, via Bassi 6, I-27100 Pavia, Italy
| | - M F Santos
- Departamento de Física, Universidade Federal de Minas Gerais, CP 702, 30123-970 Belo Horizonte, Brazil
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