[论文解读] Tensor network influence functionals for open quantum systems with general Gaussian bosonic baths

Valentin Link|arXiv (Cornell University)|Mar 24, 2026

Quantum many-body systems被引用 0

一句话总结

该论文将 TEMPO 风格的张量网络影响泛函推广到与高斯玻色子浴耦合的、具有多个非对易系统-浴耦合的开量子系统，给出一个抹平正确的、适用于长期实时仿真的 Trotter-校正高斯影响泛函。

ABSTRACT

Dynamics of open quantum systems with structured reservoirs can often be simulated efficiently with tensor network influence functionals. The standard variants of the time-evolving matrix product operator (TEMPO) method are applicable when the systems is coupled to Gaussian bosonic baths via hermitian coupling operators that mutually commute. In this work we introduce a generalization to cases where the system is coupled to a single reservoir through multiple non-commuting operators, representing the most general form of linear system-bath coupling. We construct a Gaussian influence functional that properly handles Trotter errors arising from a finite evolution time step, thus ensuring convergence for long evolution times. Based on this result, the uniform TEMPO scheme can be employed to obtain a matrix product operator form of the influence functional, enabling efficient simulations of the real-time dynamics of the open system. As a demonstration, we simulate the time evolution of driven two-level emitters coupled to a bosonic lattice at different lattice sites.

研究动机与目标

• Motivates a general Gaussian bath model with multiple non-commuting system couplings and stationary reservoirs.
• Derives a time-discretized, Trotterized influence functional that preserves Gaussian bath structure.
• Ensures convergence for long evolution times by incorporating non-trivial time-step corrections.
• Frames the result as a drop-in ingredient for TEMPO/UniTEMPO simulations.

提出的方法

• Introduce a general Gaussian bosonic bath model with L system operators S^l coupled to bath operators B^l.
• Decompose bath correlations into a Fourier-like representation to define a Gaussian auxiliary environment.
• Apply symmetric Trotterization to the total interaction to obtain time-discretized evolution with conditioned bath propagators.
• Derive an explicit form of the influence functional that includes Trotter corrections and a Gaussian (Feynman-Vernon) structure.
• Express the influence functional as a matrix product operator suitable for TEMPO/QUAPI-style contractions.
• Discuss the uniform TEMPO scheme and its suitability for long-memory baths.

实验结果

研究问题

• RQ1 How can one formulate a Gaussian influence functional for a general, potentially non-commuting set of system-bath couplings to a shared bosonic bath?
• RQ2 Can a time-discretized, Trotterized influence functional retain Gaussian bath structure and converge reliably for long evolution times?
• RQ3 How can the derived influence functional be integrated into TEMPO/UniTEMPO frameworks for scalable real-time simulations?
• RQ4 What are the practical capabilities and limitations when applying the method to driven multi-site emitter problems?

主要发现

• A time-discretized Gaussian influence functional with non-commuting couplings is derived and shown to converge with respect to the time step.
• The result preserves the Gaussian bath structure and resembles the standard Feynman-Vernon form with minimal, controllable corrections.
• The uniform TEMPO scheme can be applied to obtain an MPO form of the influence functional for efficient long-time simulations.
• The method is demonstrated with driven two-level emitters coupled to a bosonic lattice, illustrating current capabilities and limitations.
• The corrections to the time-local part due to symmetric Trotterization are explicitly identified and incorporated.