Simulating Bosonic Baths with Error Bars

TL;DR

This paper establishes rigorous error bounds for simulating bosonic baths in quantum systems, enabling more accurate and certified numerical simulations of system-environment interactions.

Contribution

It derives super-exponential Lieb--Robinson bounds and error estimates for truncating bosonic baths, improving the reliability of numerical methods like TEDOPA.

Findings

Derived super-exponential Lieb--Robinson bounds for bath truncation errors.

Provided efficient numerical monitoring of local Hilbert-space truncation errors.

Enabled fully certified simulations of system-environment interactions.

Abstract

We derive rigorous truncation-error bounds for the spin-boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths. For the numerical simulation of such baths the truncation of both, the number of modes and the local Hilbert-space dimensions is necessary. We derive super-exponential Lieb--Robinson-type bounds on the error when restricting the bath to finitely-many modes and show how the error introduced by truncating the local Hilbert spaces may be efficiently monitored numerically. In this way we give error bounds for approximating the infinite system by a finite-dimensional one. As a consequence, numerical simulations such as the time-evolving density with orthogonal polynomials algorithm (TEDOPA) now allow for the fully certified treatment of the system-environment interaction.