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International Journal of Modern Physics B

GROUND STATE ENERGY OF A TWO-LEVEL SYSTEM INTERACTING WITH PHONONS

Soma Mukhopadhyay, Bengü Demircioğlu, RAMESH GANDIKOTA, Ashok Chatterjee

Published Jul 10, 2013• 0 citations
Publisher

Abstract

A two-level system interacting with a heat bath is considered. For simplicity the electron is assumed to interact with only two modes of the heat bath. The ground state energy of this system is obtained using a variational approach involving a series of canonical transformations. The present results are found to be more accurate than the previously reported variational results.

DOI
10.1142/s0217979213500987

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A two-level system interacting with a heat bath is considered. For simplicity the electron is assumed to interact with only two modes of the heat bath. The ground state energy of this system is obtained using a variational approach involving a series of canonical transformations. The present results are found to be more accurate than the previously reported variational results.
The variational approach is applied to the study of the ground state of quantum tunneling system interacting with two phonons by use of a correlated-squeezed transformation. We fine: 1) For the two phonons bath, the ground state energy of the phonons with correlation effect is lower than that without correlation effect; 2) The effect of correlation varies with the mode parameters: In the resonant regime of the phonons and two-state system, the correlation effect is more significant and will be strengthened together with the increase of coupling coefficient.
A new variational approach is proposed to study the ground-state of a two-level system coupled to a dispersionless phonon bath. By the extended coherent state, where the more phonon correlations are easily incorporated, we can obtain very accurate ground state energy and the tunnelling reduction factor in all regime of tunnelling matrix element d0 and coupling parameter s. The relative difference between the present ones and those by exact numerical diagonalization is less then 0.001%. In addition, some simple analytical results are given in the limits of δ 0 /s ↠ 0 and ∞.
The ground state of a two-level system coupled to a dispersionless phonon bath is studied using both a connected moments expansion and a truncated Lanczos tridiagonal scheme. We consider the spin-boson Hamiltonian, $\ifmmode \hat{H}\else \^{H}\fi{}=\ensuremath{-}{\ensuremath{\delta}}_{o}{\ensuremath{\sigma}}_{x}+{\ensuremath{\sum}}_{\mathbf{k}}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathbf{k}}{a}_{\mathbf{k}}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{\mathbf{k}}+{\ensuremath{\sum}}_{\mathbf{k}}{g}_{\mathbf{k}}{(a}_{\mathbf{k}}^{\ifmmode\dagger\else\textdagger\fi{}}{+a}_{\mathbf{k}}){\ensuremath{\sigma}}_{z},$ where ${\ensuremath{\delta}}_{0}$ is the bare tunneling matrix element and gk{g}_{\mathbf{k}}gk​ represents the coupling to the k\mathbf{k}k phonon modes. Such systems have found relevance in applications to molecular polaron formation, exciton motion, and attenuation of sound in glasses. Our results are then compared to those of variational methods as well as an exact numerical diagonalization.