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arXiv · 2604.01556

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

Chu Guo·Wei Wu·Xiansong Xu·Tian Jiang·Ping-Xing Chen·Ruofan Chen
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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., $\sum_k \Aop(V_k \bdop_k + \hc)$, 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 $\sum_k (V_k\Aop\bdop_k + \hc)$, 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.

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Chu Guo, Wei Wu, Xiansong Xu, Tian Jiang, Ping-Xing Chen, Ruofan Chen. 2026-04-02. Time-evolving matrix product operators for off-diagonal system-bath coupling. https://doi.org/10.1103/6tsr-fksv

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