Effective charging energy of the single electron box

Abstract

We present numerical results on electron tunneling in a single-electron box at low temperature. The effective action of this device is equivalent to the Hamiltonian of a classical XY spin chain with long ranged interactions. Using an efficient cluster algorithm and a new transition matrix Monte Carlo approach, we are able to compute the effective charging energy $E_C^{\ast }$ in the limit of very small tunneling resistance. While previous Monte Carlo simulations were restricted to the weak and intermediate tunneling regimes, our method extends the range of $E_C^{\ast }$-values by more than 30 orders of magnitude. This allows us to clearly observe the exponential suppression of $E_C^{\ast }$ with increasing tunneling conductance $\alpha$. For large, but fixed $\alpha$, the correction to the leading exponential behavior exhibits a crossover from an intermediate temperature behavior at $\beta E_C^{\ast }\ll 1$, to zero temperature behavior at $\beta E_C^{\ast }\gg 1$. We determine this correction in both regimes and compare the numerical results to the numerous and controversial theoretical predictions for the strong tunneling limit.

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• An efficient, multiple range random walk algorithm to calculate the density of states
• Transition Matrix Monte Carlo Method
• Strong Tunneling in the Single-Electron Box
• The Single-Electron-Box and the Helicity Modulus of an inverse square XY-Model
• Strong Charge Fluctuations in the Single-Electron Box: A Quantum Monte Carlo Analysis
• Coulomb charging energy for arbitrary tunneling strength
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Cited by in corpus (2)

• Critical properties of dissipative quantum spin systems in finite dimensions
• Grand canonical partition function of a serial metallic island system