Abstract
A Monte Carlo method to study quantum systems defined on a lattice is discussed. The method is applicable to one-dimensional systems with fermion and boson degrees of freedom, as well as boson and quantum spin systems in arbitrary dimensions. It is based on a real-space break-up of the time evolution operator that yields a space-imaginary time representation of the quantum fields on a checkerboard space-time lattice. The implementation of the method is briefly discussed. We then use it to study various properties on one-dimensional models with electron-electron and electron- phonon interactions. We consider the extended Hubbard model in the ½-filled and ¼-filled band sectors. In the latter case, we focus on the behavior of the 2pF and 4pF correlation functions and discuss the relevance of our results to X-ray scattering experiments in organic charge-transfer compounds. We then study the behavior of two different electron-phonon models as a function of phonon frequency and electron-phonon coupling constant. We discuss in particular the effect of quantum fluctuations on the Peierls instability, and the role of the number of components of the electron spin.
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© 1984 D. Reidel Publishing Company, Dordrecht, Holland
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Hirsch, J.E. (1984). Numerical Simulation of Quantum Lattice Systems: Electron-Electron and Electron-Phonon Interactions in One Dimension. In: Kalos, M.H. (eds) Monte Carlo Methods in Quantum Problems. NATO ASI Series, vol 125. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6384-9_14
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DOI: https://doi.org/10.1007/978-94-009-6384-9_14
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