Abstract
The spin-boson (SB) model plays a central role in studies of dissipative quantum dynamics, due to bothits conceptual importance and relevance to a number of physical systems. Here, we provide rigorous bounds of the computational complexity of the SB model for the physically relevant case of a zero temperature ohmic bath. We start with the description of the bosonic bath via its Feynman-Vernon influence functional (IF), which is a tensor on the space of the trajectory of an impurity spin. By expanding the kernel of the IF via a sum of decaying exponentials, we obtain an analytical approximation of the continuous bath by a finite number of damped bosonic modes. We bound the error induced by restricting bosonic Hilbert spaces to a finite-dimensional subspace with small boson numbers, which yields an analytical form of a matrix-product state (MPS) representation of the IF. We show that the MPS bond dimension D scales polynomially in the error on physical observables as well as in the evolution time T, . This bound indicates that the SB model can be efficiently simulated using a polynomial in time-computational resources.
- Received 4 August 2023
- Revised 21 January 2024
- Accepted 12 April 2024
DOI:https://doi.org/10.1103/PhysRevB.109.205126
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