Journal of Physics Condensed Matter

The localisation transition in a dissipative two-state system: a squeezed state approach

Yumei Zhang, Hong Chen, Xiang Xia Wu

Published Apr 2, 1990• 3 citations

Abstract

A displaced squeezed state is used as the variational ground state of a spin-boson Hamiltonian describing the interaction of a two-state system with a phonon bath. The phase diagram for localisation in the ohmic dissipation is obtained by a method based on the self-consistent calculation of the effective tunnelling splitting. A comparison with the results of the usual displaced state approximation and the renormalisation group theory is also given.

DOI: 10.1088/0953-8984/2/13/021

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Journal of Physics Condensed Matter

The localisation transition in a dissipative two-state system: a squeezed state approach

Yumei Zhang, Hong Chen, Xiang Xia Wu

Published Apr 2, 1990• 3 citations

Publisher

Abstract

DOI: 10.1088/0953-8984/2/13/021

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{\mathit{tsum}}_{\mathit{l}}

{\mathit{g}}_{\mathit{l}}^{2}

\ensuremath{\delta}(\ensuremath{\omega}-${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$), but also on the explicit form of the coupling strength

{\mathit{g}}_{\mathit{l}}

\ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}^{\ensuremath{\lambda}}$ (${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$ is the phonon frequency). For weak coupling (\ensuremath{\lambda}\ensuremath{\ge}1), the effect of displacement of the phonon state is dominant; while for strong couplings (\ensuremath{\lambda}1), one must take account of both displacement and deformation. Displaced squeezed states are proposed as ground states of the bath under strong coupling,and we show that the localization transition of the Ohmic dissipation occurs at ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$=3-2\ensuremath{\lambda} instead of ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$=1 as for the weak-coupling case.

{\mathit{g}}_{\mathit{l}}

\ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}^{\ensuremath{\lambda}}$ (${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$ is the phonon frequency) is analyzed. We find that, in the strong-coupling region, the displaced-squeezed state is more stable and the ground-state properties depend not only on the spectral density but also on the index \ensuremath{\lambda}. Moreover, we find that the stable area of the displaced-squeezed state increases as \ensuremath{\lambda} decreases.