Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems pp 119-122 | Cite as

# Summary

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## Abstract

In this thesis, we have developed the novel Monte Carlo methods and investigated precisely the critical phenomena of the spin-Peierls systems. The key theme is that the quantum lattice fluctuation introduces the spin frustration. The concept of the Peierls transition originates from the simple but drastic property about the instability to dimerization of the one-dimensional metal as early as 50’s. The lattice degree of freedom, there, was treated *adiabatically*; that is, it was approximated as a classical parameter.

### Keywords

General improvement of Markov chain Monte Carlo Extended directed-loop algorithm Quantum Monte Carlo level spectroscopy Frustrated quantum spin system### References

- 1.Hase, M., Terasaki, I., & Uchinokura, K. (1993). Observation of the spin-Peierls transition in linear Cu\(^{2+}\) (spin-\(\frac{1}{2})\) chains in an inorganic compound CuGeO\(_3\).
*Physical Review Letters*,*70*, 3651.ADSCrossRefGoogle Scholar - 2.Nomura, K., & Okamoto, K. (1994). Critical properties of \(S=\frac{1}{2}\) antiferromagnetic
*XXZ*chain with next-nearest-neighbour interactions.*Journal of Physics A: Mathematical and General*,*27*, 5773.Google Scholar - 3.Sun, P., Schmeltzer, D., & Bishop, A. R. (2000). Analytic approach to the one-dimensional spin-Peierls system in the entire frequency range.
*Physical Review B*,*62*, 11308–11311.Google Scholar

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© Springer Japan 2014