2020
DOI: 10.1063/5.0018149
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A general automatic method for optimal construction of matrix product operators using bipartite graph theory

Abstract: Constructing matrix product operators (MPOs) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For the DMRG to be conveniently used in different problems described by different Hamiltonians, in this work, we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) it is automatic in that only the definition of … Show more

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Cited by 43 publications
(63 citation statements)
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“…To calculate C ( t ), , and are propagated in real time to obtain and and then C ( t ) is calculated by: Here the current operator is represented as an MPO and inner-product for includes tracing over both P space and Q space. The construction of the MPOs is performed in an automatic and optimal fashion through our recently proposed algorithm 46 . Note that different from the simulation of diffusion dynamics, the initial state of the formulation does not require electronic excitation from the zero electron manifold.…”
Section: Methodsmentioning
confidence: 99%
“…To calculate C ( t ), , and are propagated in real time to obtain and and then C ( t ) is calculated by: Here the current operator is represented as an MPO and inner-product for includes tracing over both P space and Q space. The construction of the MPOs is performed in an automatic and optimal fashion through our recently proposed algorithm 46 . Note that different from the simulation of diffusion dynamics, the initial state of the formulation does not require electronic excitation from the zero electron manifold.…”
Section: Methodsmentioning
confidence: 99%
“…(2) (4)) in the previous section can be constructed into MPOs using the automatic construction algorithm proposed in our former work. 43…”
Section: Td-dmrg Quantum Dynamics Methodsmentioning
confidence: 99%
“…To construct the MPO for the system Hamiltonian, we use the symbolic method developed in our former work 46 to first construct the symbolic MPO and then expand every operator on the primitive basis to obtain a numerical one. The site ordering is another key aspect of a DMRG calculation.…”
Section: A Two-mode Model With Morse Potentialmentioning
confidence: 99%
“…[33][34][35][36] In recent years, TD-DMRG has emerged as a powerful method to simulate large-scale full-quantum dynamics, [37][38][39][40][41][42][43][44] such as electronic spectroscopy of molecular aggregates, real-time internal conversion in pyrazine, carrier mobility in one-dimensional molecular crystal, etc. There are several advantages of TD-DMRG compared to the other numerical methods: (i) The accuracy could be systematically improved by a single parameter; (ii) The Hamiltonian that can be handled is flexible once it could be represented in a sum-of-products (SOP) form 45,46 and thus TD-DMRG could handle both model anharmonic PES and PES of real molecules after fitting or re-fitting to an SOP form; 47,48 (iii) The scaling of computational cost is polynomial with system size and thus it is scalable for polyatomic molecules; (iv) The time evolution of wavefunction (at zero temperature) and density matrix (at finite temperature) could be simulated in the same framework. 49,50 These advantages make TD-DMRG a suitable method to calculate the molecular NRER rates.…”
Section: Introductionmentioning
confidence: 99%