Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations

TL;DR

This paper develops an analytical approach to study non-canonical equilibrium quantum statistics in a spin-boson model, valid for arbitrary temperature and system-bath coupling strength, confirmed by exact Monte Carlo simulations.

Contribution

It introduces a combined polaron transformation and perturbation theory method to analyze non-canonical statistics in a spin-boson model across all coupling regimes.

Findings

Non-canonical statistics increase as temperature decreases.

Non-canonical effects vanish at high temperature.

Theoretical results agree with Monte Carlo simulations.

Abstract

Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study non-canonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte-Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify non-canonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, non-canonical statistics enhances as temperature decreases but vanishes at high temperature.