Phonons and the Isotopically Induced Mott transition - Physics

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Phonons and the Isotopically Induced Mott transition - Physics

(a)

n = 2

(a)

(b)

n = 3

(b)

Figure 5.6

The energy ratio E Nmax /E 100 for (a) n=2 and (b) n=3 for various coupling strengths and within

different e-ph energy regimes where N max is the number of phonons involved in the exact

diagonalization. The energy ratio converges to 1 within all regimes for N max >60.

Figure 5.7

(a) The wavefunction overlap of the effective and exact Holstein Hamiltonians for n=2 (solid

line) and n=3 (dashed line) in various e-ph energy regimes ( ◊ - ω/t = 0.01, o - ω/t=0.1,

× - ω/t=1 , * - ω/t=10 ) . These show that the overlap falls away dramatically with both

increasing gω and decreasing adiabacity. (b) The ratio of effective to exact energies showing

diverging agreement with increasing gω and decreasing adiabacity. INSETS show the

behaviour in the regime relevant to κ-(ET) 2 Br

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