Transient dynamical phase diagram of the spin-boson model

TL;DR

This paper uses an advanced quantum Monte Carlo method to explore the real-time dynamics of the sub-Ohmic spin-boson model, revealing a dynamical phase diagram that differs from the equilibrium one and identifying mechanisms for the transition from coherent to incoherent behavior.

Contribution

It provides the first numerically exact dynamical phase diagram of the sub-Ohmic spin-boson model, highlighting differences from the equilibrium phase diagram and analyzing crossover mechanisms.

Findings

Dynamical phase diagram differs from equilibrium phase diagram.

Identified damping as a mechanism for crossover in the sub-Ohmic regime.

Oscillation frequency drops to zero near the transition in the Ohmic regime.

Abstract

We investigate the real-time dynamics of the sub-Ohmic spin-boson model across a broad range of coupling strengths, using the numerically exact inchworm quantum Monte Carlo algorithm. From short- and intermediate-time dynamics starting from an initially decoupled state, we extract signatures of the zero-temperature quantum phase transition between localized and delocalized states. We show that the dynamical phase diagram thus obtained differs from the equilibrium phase diagram in both the values of critical couplings and the associated values of the critical exponent. We also identify and quantitatively analyze two competing mechanisms for the crossover between coherent oscillations and incoherent decay. Deep in the sub-Ohmic regime, the crossover is driven by the damping of the oscillation amplitude, while closer to the Ohmic regime the oscillation frequency itself drops sharply to zero at large coupling.