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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