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Physical Review Research

Efficient time-dependent dynamics of matrix product states using average Hamiltonians

Belal Abouraya, Jirawat Saiphet, Fedor Jelezko, Ressa S. Said

Published Oct 6, 2026• 0 citations
Publisher
DOI
10.1103/cxv4-r2bs

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Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor networks have been an essential tool for studying such quantum systems, owing to their ability to efficiently capture the entanglement properties of the systems they represent. One of the well-known tensor network architectures, namely matrix product states (MPS), is the standard method for simulating one-dimensional QMBS. Here, we propose a simple, yet efficient, method to augment the already available MPS algorithms to simulate the dynamics of time-dependent Hamiltonians with better accuracy and a faster convergence rate, giving a second-order convergence compared to the first-order convergence of the standard method. We apply our proposed method to simulate the dynamics of a chain of single spins associated with nitrogen-vacancy color centers in diamonds, which has potential applications for practical and scalable quantum technologies, and find that our method improves the average error for a system of few NV centers by a factor of about 1000 for moderate step sizes. Our work paves the way for efficient simulation of QMBS under the influence of time-dependent Hamiltonians.
We present a Hierarchical Equations of Motion (HEOM) approach in the Matrix Product State (MPS) formalism to simulate carrier transport in molecular aggregates described by an electron-phonon Hamiltonian with bosonic dissipation. Transport properties are evaluated through time-dependent population analysis and mobility calculations. The method's validity is rigorously established through benchmarking against conventional HEOM. Comparative analysis with Thermo-Field Dynamics combined with MPS (TFD + MPS) reveals fundamental similarities and differences in their effective Hamiltonians and demonstrates the superior accuracy and computational efficiency of our HEOM + MPS framework. For single-electron systems, we introduce state-vector space configurations that enhance performance beyond traditional Fock space approaches. Results confirm that our method provides a robust, nearly exact, and efficient numerical quantum dynamic approach for carrier transport in dissipative bosonic environments.
Matrix product state (MPS) is one efficient way to compress quantum states and reduce computational cost. This chapter presents the application of MPS framework as well as time-dependent density matrix renormalization group (tDMRG) variants in chemical systems. The elementary principles of MPS approaches are provided, including the basic concept of MPS and matrix product operator, the density matrix renormalization group method and tDMRG approaches based on the MPS/matrix product operator framework to solve the time-independent and dependent Schrödinger equation, respectively. Then, several examples of tDMRG applications in chemical systems investigated by the authors, including charge carrier dynamics in polymer chain, charge transfer and dissociation in organic systems, nonadiabatic dynamics of excited states S1/S2 in pyrazine molecule and singlet fission processes in organic systems, are displayed.