Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model

TL;DR

This paper introduces a novel numerical method combining polynomial spectral function expansions with sparse grid techniques to efficiently analyze dissipative quantum systems, exemplified by the spin-boson model.

Contribution

The authors develop a new approach that constructs a manageable Hilbert space for bath degrees of freedom, enabling accurate simulations of open quantum systems with standard diagonalization methods.

Findings

Accurately captures phase transition and critical behavior.

Effectively models dissipative spin dynamics.

Demonstrates efficiency and precision in complex quantum calculations.

Abstract

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behaviour, and dissipative spin dynamics in the spin boson model