Langevin Simulations of a Long Range Electron Phonon Model

We present a Quantum Monte Carlo (QMC) study, based on the Langevin equation, of a Hamiltonian describing electrons coupled to phonon degrees of freedom. The bosonic part of the action helps control the variation of the field in imaginary time. As a consequence, the iterative conjugate gradient solution of the fermionic action, which depends on the boson coordinates, converges more rapidly than in the case of electron-electron interactions, such as the Hubbard Hamiltonian. Fourier Acceleration is shown to be a crucial ingredient in reducing the equilibration and autocorrelation times. After describing and benchmarking the method, we present results for the phase diagram focusing on the range of the electron-phonon interaction. We delineate the regions of charge density wave formation from those in which the fermion density is inhomogeneous, caused by phase separation. We show that the Langevin approach is more efficient than the Determinant QMC method for lattice sizes $N \gtrsim 8 \times 8$ and that it therefore opens a potential path to problems including, for example, charge order in the 3D Holstein model

Geometric frustration in the mixed layer pnictide oxides

We present results from a Monte Carlo investigation of a simple bilayer model with geometrically frustrated interactions similar to those found in the mixed layer pnictide oxides $(Sr_{2}Mn_{3}Pn_{2}O_{2}, Pn=As,Sb).$ Our model is composed of two inequivalent square lattices with nearest neighbor intra- and interlayer interactions. We find a ground state composed of two independent N\'{e}el ordered layers when the interlayer exchange is an order of magnitude weaker than the intralayer exchange, as suggested by experiment. We observe this result independent of the number of layers in our model. We find evidence for local orthogonal order between the layers, but it occurs in regions of parameter space that are not experimentally realized. We conclude that frustration caused by nearest neighbor interactions in the mixed layer pnictide oxides is not sufficient to explain the long--range orthogonal order that is observed experimentally, and that it is likely that other terms (e.g., local anisotropies) in the Hamiltonian are required to explain the magnetic behavior.Comment: Revetex, 4 pages, 3 figures, to appear in the proceedings of "HFM 2000" (Waterloo, June 2000); submitted to Can. J. Phy

Geometric frustration in the mixed layer pnictide oxides

We present results from a Monte Carlo investigation of a simple bilayer model with geometrically frustrated interactions similar to those found in the mixed layer pnictide oxides $(Sr_{2}Mn_{3}Pn_{2}O_{2}, Pn=As,Sb).$ Our model is composed of two inequivalent square lattices with nearest neighbor intra- and interlayer interactions. We find a ground state composed of two independent N\'{e}el ordered layers when the interlayer exchange is an order of magnitude weaker than the intralayer exchange, as suggested by experiment. We observe this result independent of the number of layers in our model. We find evidence for local orthogonal order between the layers, but it occurs in regions of parameter space that are not experimentally realized. We conclude that frustration caused by nearest neighbor interactions in the mixed layer pnictide oxides is not sufficient to explain the long--range orthogonal order that is observed experimentally, and that it is likely that other terms (e.g., local anisotropies) in the Hamiltonian are required to explain the magnetic behavior.Comment: Revetex, 4 pages, 3 figures, to appear in the proceedings of "HFM 2000" (Waterloo, June 2000); submitted to Can. J. Phy