Time-evolving matrix product operators for off-diagonal system-bath coupling

2026/04/30 by Anonymous, Chu Guo, Wei Wu +4
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #cond-mat.mes-hall

paper · pdf · doi:10.1103/6tsr-fksv

21 pages, 12 figures

openalex publication_date 2026/07/29 · arxiv created 2026/07/30 · openalex created_date 2026/07/30 · openalex updated_date 2026/07/30 · arxiv updated 2026/07/31

Abstract

The time-evolving matrix product operator (TEMPO) method has proven to be a powerful method to study the long-time dynamics of bosonic impurity problems where a small system is linearly coupled to a noninteracting bosonic bath. However, current developments of TEMPO have mostly focused on the case of diagonal system-bath coupling, i.e., ∑_k \Aop(V_k \bdop_k + \hc), with \Aop a Hermitian operator of the system. Based on the process tensor framework, we extend TEMPO to the more general case of off-diagonal system-bath coupling in the form ∑_k (V_k\Aop\bdop_k + \hc), where \Aop could be non-Hermitian. As applications, we study the real-time dynamics of a spin that is coupled to a sub-ohmic bath via the Jaynes-Cummings-type system-bath coupling and compare it against the standard spin-boson model, where we show that the commonly used rotating-wave approximation could be very poor for this bath. We also study the imaginary-time evolution of a bosonic impurity with nonzero on-site interaction that is coupled to a sub-ohmic bath, to illustrate the flexibility of our method. Our method provides a unified framework to understand different variants of TEMPO, and is a promising building block for an impurity solver in the bosonic dynamical mean field theory for the normal phase with a scalar hybridization function.

Citations

• Path Integral Formalism for Quantum Open Systems
• Time evolving matrix product operator (TEMPO) method in a non-diagonal basis set based on derivative of the path integral expression
• Efficient Pseudomode Representation and Complexity of Quantum Impurity Models
• Randomised benchmarking for characterizing and forecasting correlated processes
• A bound on approximating non-Markovian dynamics by tensor networks in the time domain
• The density-matrix renormalization group in the age of matrix product states
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Non-Markovian Open Quantum Systems
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Dynamics of the dissipative two-state system

Related

• Time evolving matrix product operator (TEMPO) method in a non-diagonal basis set based on derivative of the path integral expression
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• A bound on approximating non-Markovian dynamics by tensor networks in the time domain
• An Impurity Solver Using the Time-Dependent Variational Matrix Product State Approach
• Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States