Variational Approach to the Spin-boson Model With a Sub-Ohmic Bath

TL;DR

This paper investigates how dissipation affects quantum tunneling in the spin-boson model with a sub-Ohmic bath using a variational approach, revealing a discontinuous phase transition and clarifying the true critical point.

Contribution

It introduces a variational method to analyze the phase transition in the sub-Ohmic spin-boson model, distinguishing the thermodynamic critical point from the crossover point.

Findings

Discontinuous transition scenario in sub-Ohmic dissipation

The true crossover point differs from the thermodynamic critical point

Phase diagram aligns with numerical renormalization group results

Abstract

The influence of dissipation on quantum tunneling in the spin-boson model with a sub-Ohmic bath is studied by a variational calculation. By examining the evolution of solutions of the variational equation with the coupling strength near the phase boundary, we are able to present a scenario of discontinuous transition in sub-Ohmic dissipation case in accord with Ginzburg-Landau theory. Based on the constructed picture, it is shown that the critical point found in the general way is not thermodynamically the critical point, but the point where the second energy minimum begins to develop. The true cross-over point is calculated and the obtained phase diagram is in agreement with the result of numerical renormalization group calculation.