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Oz A, Nitzan A, Hod O, Peralta JE. Electron Dynamics in Open Quantum Systems: The Driven Liouville-von Neumann Methodology within Time-Dependent Density Functional Theory. J Chem Theory Comput 2023; 19:7496-7504. [PMID: 37852250 PMCID: PMC10653109 DOI: 10.1021/acs.jctc.3c00311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Indexed: 10/20/2023]
Abstract
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville-von Neumann methodology is used to impose open boundary conditions on finite model systems whose dynamics is described using time-dependent density functional theory. As a proof of concept, the developed methodology is applied to simple spin-compensated model systems, including a hydrogen chain and a graphitic molecular junction. Good agreement between steady-state total currents obtained via direct propagation and those obtained from the self-consistent solution of the corresponding Sylvester equation indicates the validity of the implementation. The capability of the new computational approach to analyze, from first principles, non-equilibrium dynamics of open quantum systems in terms of temporally and spatially resolved current densities is demonstrated. Future extensions of the approach toward the description of dynamical magnetization and decoherence effects are briefly discussed.
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Affiliation(s)
- Annabelle Oz
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
| | - Abraham Nitzan
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
- Department
of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19103, United States
| | - Oded Hod
- Department
of Physical Chemistry, School of Chemistry, the Raymond and Beverly
Sackler Faculty of Exact Sciences, and the Sackler Center for Computational
Molecular and Materials Science, Tel Aviv
University, Tel Aviv, 6997801, Israel
| | - Juan E. Peralta
- Department
of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, United States
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Head-Marsden K, Flick J, Ciccarino CJ, Narang P. Quantum Information and Algorithms for Correlated Quantum Matter. Chem Rev 2020; 121:3061-3120. [PMID: 33326218 DOI: 10.1021/acs.chemrev.0c00620] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.
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Affiliation(s)
- Kade Head-Marsden
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Johannes Flick
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Christopher J Ciccarino
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States.,Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Prineha Narang
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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Raeber AE, Mazziotti DA. Non-equilibrium steady state conductivity in cyclo[18]carbon and its boron nitride analogue. Phys Chem Chem Phys 2020; 22:23998-24003. [DOI: 10.1039/d0cp04172f] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
A ring-shaped carbon allotrope was recently synthesized for the first time, reinvigorating theoretical interest in this class of molecules.
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Affiliation(s)
- Alexandra E. Raeber
- Department of Chemistry and The James Franck Institute
- The University of Chicago
- Chicago
- USA
| | - David A. Mazziotti
- Department of Chemistry and The James Franck Institute
- The University of Chicago
- Chicago
- USA
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Head-Marsden K, Mazziotti DA. Satisfying fermionic statistics in the modeling of non-Markovian dynamics with one-electron reduced density matrices. J Chem Phys 2019; 151:034111. [PMID: 31325953 DOI: 10.1063/1.5100143] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Treatment of Markovian, many-electron dynamics from the solution of the Lindblad equation for the 1-electron reduced density matrix requires additional constraints on the bath operators to maintain fermion statistics. Recently, we generalized Lindblad's formalism to non-Markovian dynamics through an ensemble of Lindbladian trajectories. Here we show that the fermion statistics of non-Markovian dynamics can be enforced through analogous constraints on the bath operators of each Lindbladian trajectory in the ensemble. To illustrate, we apply the non-Markovian method to three distinct systems of two fermions in three levels. While the electrons violate the fermion statistics without the constraints, correct fermion behavior is recovered with the constraints.
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Affiliation(s)
- Kade Head-Marsden
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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Oz I, Hod O, Nitzan A. Evaluation of dynamical properties of open quantum systems using the driven Liouville-von Neumann approach: methodological considerations. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1584338] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Inbal Oz
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
| | - Oded Hod
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
| | - Abraham Nitzan
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA, USA
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Raeber AE, Mazziotti DA. Current-constrained one-electron reduced density-matrix theory for non-equilibrium steady-state molecular conductivity. Phys Chem Chem Phys 2019; 21:12620-12624. [DOI: 10.1039/c9cp01678c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In the effort to create ever smaller electronic devices, the idea of single molecule circuit elements has sparked the imagination of scientists for nearly fifty years.
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Affiliation(s)
- Alexandra E. Raeber
- Department of Chemistry and The James Franck Institute
- The University of Chicago
- Chicago
- USA
| | - David A. Mazziotti
- Department of Chemistry and The James Franck Institute
- The University of Chicago
- Chicago
- USA
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Current-constrained density-matrix theory to calculate molecular conductivity with increased accuracy. Commun Chem 2018. [DOI: 10.1038/s42004-018-0030-2] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022] Open
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Schlimgen AW, Mazziotti DA. Static and Dynamic Electron Correlation in the Ligand Noninnocent Oxidation of Nickel Dithiolates. J Phys Chem A 2017; 121:9377-9384. [DOI: 10.1021/acs.jpca.7b09567] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Anthony W. Schlimgen
- Department of Chemistry and
the James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
| | - David A. Mazziotti
- Department of Chemistry and
the James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
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Hod O, Rodríguez-Rosario CA, Zelovich T, Frauenheim T. Driven Liouville von Neumann Equation in Lindblad Form. J Phys Chem A 2016; 120:3278-85. [PMID: 26807992 DOI: 10.1021/acs.jpca.5b12212] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The Driven Liouville von Neumann approach [J. Chem. Theory Comput. 2014, 10, 2927-2941] is a computationally efficient simulation method for modeling electron dynamics in molecular electronics junctions. Previous numerical simulations have shown that the method can reproduce the exact single-particle dynamics while avoiding density matrix positivity violation found in previous implementations. In this study we prove that in the limit of infinite lead models the underlying equation of motion can be cast in Lindblad form. This provides a formal justification for the numerically observed density matrix positivity conservation.
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Affiliation(s)
- Oded Hod
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University , Tel Aviv 6997801, Israel
| | - César A Rodríguez-Rosario
- Bremen Center for Computational Materials Science, University of Bremen , Am Falturm 1, Bremen, 28359, Germany
| | - Tamar Zelovich
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University , Tel Aviv 6997801, Israel
| | - Thomas Frauenheim
- Bremen Center for Computational Materials Science, University of Bremen , Am Falturm 1, Bremen, 28359, Germany
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Head-Marsden K, Mazziotti DA. Communication: satisfying fermionic statistics in the modeling of open time-dependent quantum systems with one-electron reduced density matrices. J Chem Phys 2015; 142:051102. [PMID: 25662627 DOI: 10.1063/1.4906942] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
For an open, time-dependent quantum system, Lindblad derived the most general modification of the quantum Liouville equation in the Markovian approximation that models environmental effects while preserving the non-negativity of the system's density matrix. While Lindblad's modification is correct for N-electron density matrices, solution of the Liouville equation with a Lindblad operator causes the one-electron reduced density matrix (1-RDM) to violate the Pauli exclusion principle. Consequently, after a short time, the 1-RDM is not representable by an ensemble N-electron density matrix (not ensemble N-representable). In this communication, we derive the necessary and sufficient constraints on the Lindbladian matrix within the Lindblad operator to ensure that the 1-RDM remains N-representable for all time. The theory is illustrated by considering the relaxation of an excitation in several molecules F2, N2, CO, and BeH2 subject to environmental noise.
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Affiliation(s)
- Kade Head-Marsden
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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Zelovich T, Kronik L, Hod O. State Representation Approach for Atomistic Time-Dependent Transport Calculations in Molecular Junctions. J Chem Theory Comput 2014; 10:2927-41. [PMID: 26588268 DOI: 10.1021/ct500135e] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
We propose a new method for simulating electron dynamics in open quantum systems out of equilibrium, using a finite atomistic model. The proposed method is motivated by the intuitive and practical nature of the driven Liouville-von-Neumann equation approach of Sánchez et al. [J. Chem. Phys. 2006, 124, 214708] and Subotnik et al. [J. Chem. Phys. 2009, 130, 144105]. A key ingredient of our approach is a transformation of the Hamiltonian matrix from an atomistic to a state representation of the molecular junction. This allows us to uniquely define the bias voltage across the system while maintaining a proper thermal electronic distribution within the finite lead models. Furthermore, it allows us to investigate complex molecular junctions, including multilead configurations. A heuristic derivation of our working equation leads to explicit expressions for the damping and driving terms, which serve as appropriate electron sources and sinks that effectively "open" the finite model system. Although the method does not forbid it, in practice we find neither violation of Pauli's exclusion principles nor deviation from density matrix positivity throughout our numerical simulations of various tight-binding model systems. We believe that the new approach offers a practical and physically sound route for performing atomistic time-dependent transport calculations in realistic molecular junction models.
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Affiliation(s)
- Tamar Zelovich
- Department of Chemical Physics, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 69978, Israel
| | - Leeor Kronik
- Department of Materials and Interfaces, Weizmann Institute of Science , Rehovoth 76100, Israel
| | - Oded Hod
- Department of Chemical Physics, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 69978, Israel
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Mazziotti DA. Two-Electron Reduced Density Matrix as the Basic Variable in Many-Electron Quantum Chemistry and Physics. Chem Rev 2011; 112:244-62. [DOI: 10.1021/cr2000493] [Citation(s) in RCA: 124] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- David A. Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
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13
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Greenman L, Mazziotti DA. Balancing single- and multi-reference correlation in the chemiluminescent reaction of dioxetanone using the anti-Hermitian contracted Schrödinger equation. J Chem Phys 2011; 134:174110. [DOI: 10.1063/1.3585691] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Dzhioev AA, Kosov DS. Super-fermion representation of quantum kinetic equations for the electron transport problem. J Chem Phys 2011; 134:044121. [DOI: 10.1063/1.3548065] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
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