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Perturbative Quantum Monte Carlo Study of LiHoF4 in a Transverse Magnetic Field
Physical Review B (2008)
  • S. M. Ali Tabei, University of Northern Iowa
  • M.J.P. Gingras
  • Y.J. Kao
  • T. Yavors'kii
Results from a recent quantum Monte Carlo (QMC) study [P. B. Chakraborty et al., Phys. Rev. B 70, 144411 (2004)] of a model of the LiHoF4 Ising magnetic material in an external transverse magnetic field, Bx, show a discrepancy with experimental results, even for small Bx where quantum fluctuations are small. This discrepancy persists asymptotically close to the classical ferromagnet to paramagnet phase transition. In this paper, we numerically reinvestigate the temperature T versus transverse-field phase diagram of LiHoF4 in the regime of weak Bx. In this regime, starting from an effective low-energy spin-1/2 description of LiHoF4, we apply a cumulant expansion to derive an effective temperature-dependent classical Hamiltonian that incorporates perturbatively the small quantum fluctuations in the vicinity of the classical phase transition at Bx=0. Via this effective classical Hamiltonian, we study the BxT phase diagram via classical Monte Carlo simulations. In particular, we investigate the influence on the phase diagram of various effects that may be at the source of the discrepancy between the previous QMC results and the experimental ones. In particular, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the BxT phase diagram is modified when using different microscopic crystal-field Hamiltonians. The main conclusion of our work is that we fully reproduce the previous QMC results at small Bx. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a BxT phase diagram compatible with the experiments in the quasiclassical small Bx regime.
Publication Date
November 11, 2008
Citation Information
S. M. Ali Tabei, M.J.P. Gingras, Y.J. Kao and T. Yavors'kii. "Perturbative Quantum Monte Carlo Study of LiHoF4 in a Transverse Magnetic Field" Physical Review B Vol. 78 Iss. 11 (2008)
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