Quantum Monte Carlo Level Spectroscopy

Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

The new method of analysis combining the level spectroscopy and the quantum Monte Carlo method will be developed in this chapter. The finite-size scaling method performs well and elicits the universality class correctly for many continuous phase transitions. However, for the Kosterlitz-Thouless transition where the correlation length exponentially diverges at the critical point, this conventional scaling method does not work practically because exponentially large systems need to be calculated. For overcoming the difficulty of the analysis, the level spectroscopy was invented. This method has been combined with the diagonalization so far; the application has been restricted to small-size systems. For the combination with the Monte Carlo method, the precise gap calculation is inevitable. Thus, we will devise an improved gap estimator that can overcome the notorious difficulty of the numerical inverse Laplace transformation. We will demonstrate the effectiveness for the spin-Peierls model and the \(\mathrm{S}=1\) alternating bond model. The quantum Monte Carlo technique for the twisted boundary condition for detecting the transition point will also be presented.

Keywords

Level spectroscopy Improved gap estimator Inverse Laplace transformation 

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of PhysicsBoston UniversityBostonUSA

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